Calculus 1 – Math6100: By: Grace, Francheska, Cute, Kuya Lodi, Boss Franz

CALCULUS 1 – MATH6100 By: Grace, Francheska, Cute, Kuya Lodi, Boss Franz Sketch the lines X=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew. =a. The slope of the tangent lines at x=1 is 1 and at x=3 is -1. =e. The slope of the tangent line x=2 is 0. The slope of a horizontal line is =0 . (Answer should be numeric) The process of taking the limit of a sum of little quantities is called = integration If a tangent line is inclined 45 degrees, then what is the slope the tangent line? = d. 1 The following problems could be solved by differential calculus: =a. rate or speed =b. largest or smallest volume of a solid The slope of the tangent line is called the =derivative of the function f(x) at point P. Sketch the lines x=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew. Select one or more: =a. The slope of the tangent line at x=2 is 0. =b. The slope of the tangent lines at x=1 is 1 and at x=3 is -1. Calculus was developed by Leibniz and =newton . (Indicate only the last name) The 2 divisions of Calculus are: Select one or more:

a. Differential b. Integral

The slope of a vertical line is Undefined

Find the slope of the line passing through the points (3,-4) and (-6,9). Use decimal value for your final answer. =-1.44

Find the equation of the line which goes through the point (3,10) and is parallel to the line 7xy=1.

=7 x-y – 11 = 0 Find the equation of a circle with radius=6 and center C(2,-5). (write the required exponent after the ^ symbol; write the numerical coefficient of each term to complete the required equation)

=x^ 2 +y^ 2 – 4 x + 10 y -7 = 0 Find the slope and midpoint of the line segment from P(2,-3) to Q(2+n,-3+5n).

=slope = 5 midpoint(0.5n+ 2, 2.5 n-3) Find the slope of the line which is tangent to the circle with center C(3,1) at the point P(8,13). =slope of the tangent line = -5/ 12

Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x=2. (write the numerical coefficient of each term to complete the required equation)

= 3 x + 7 y + 29 = 0 Find the length and midpoint of the interval from x=9 to x=-2. (use decimal values for fractional answer)

=length = 11 and midpoint x = 3.5 Find the equation of the line passing through (-2,3) and perpendicular to the line 4x=9-2y. Use the general equation of the line for your final answer.

=x – 2 y + 8 = 0 Find an equation describing all points P(x,y) equidistant from Q(-3,4) and R(1,-3). (use the general equation of a line - input the numerical coefficient of each term of the equation below)

=8 x- 14 y + 15 = 0

The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=10 to t=30 seconds? (b) What was the average velocity of the car from t=20 to t=25 seconds? a) average velocity = Answer (b) average velocity = Answer

feet/second feet/second

The figure shows the temperature during a day in a place. How fast is the temperature changing from 1:00 P.M. to 7:00 P.M.? Round-off your answer to 2 decimal places. Answer: Answer

0

F/hour

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1) Answers: (a) A(2.5) = Answer (b) A(4) - A(1) = Answer

square units square units

For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o f(x). Note: For exponential answer, express it like x^3 for x cubed. Use lowercase letters, and do not put spaces in your answer. Answer: f o g(x) = Answer g o f(x) = Answer

3x^2+1 9x^2-12x+5

Refer to the figure. Which of the following represents the graph drawn in red? Select one: a. | g(x) | b. g(x-1) c. [ g(x) ] d. g(x)-1

An enrollment slip indicates a specific down payment based from the number of units enrolled by a student as follows: for number of units from 1 to 9, down payment is Php 5000; for number of units from 10 to 15, down payment is Php 10,000; and a down payment of Php 15,000 for units from 16 to 21. Which of the multiline functions define E(d), the down payment due on specific number of units enrolled. Unit is of integer type.

Evaluate f(3), g(-1), and h(4). Answer: f(3) = Answer g(-1) = Answer h(4) = Answer After evaluating g(-4), g(-1) and g(3), choose which graph represents the given conditions.

Answer:

A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function for T(x), the state income tax due on earnings of x dollars.

Answer:

Given g(x) = (x+3)/(x-1). Evaluate g(5) and g(2n+1). Note that fractional answers must be expressed like -5/6, and answers with exponents like (x^2-1)/(x+3). Use lower case letters.and do not use spaces in your answers. Answer: g(5) =Answer

and g(2n+1) =Answer

A function f is given by f(7-11x) = 3x3 - 10x. Evaluate f(-4). Answer: f(-4) =Answer A FUNCTION assigns a unique output element in the range to each input element from the domain.

For y=f(x), x is the domain, and y is the range

Given f(x) = x3 - 4x2 +2, f(2) when evaluated is -6.

Which of the following figures represents the graph of a function?

Select one: a. Figures 1 and 2 b. Figure 2 c. Figure 1 d. Figure 3 e. All of the figures f. Figures 1 and 3

Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)). Note: Do not use spaces in your answers. Answer: (Write your answer in this format: x+A+1) f(g(x)) =Answer g(f(x)) =Answer A =Answer

For f(x) = |9-x| and g(x) = sqrt(x-1). Evaluate fog(1). Answer: f(g(1) =Answer

Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any. Answers: (a) Answer (b) Answer (c) Answer (d) Answer

Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = Answer

From the figure shown, find the values of f(2), f(-1) and f(0). Answers: f(2) =Answer f(-1) =Answer f(0) =Answer

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1). Answers: f(-3) = Answer f(-1) = Answer f(0) = Answer f(1) = Answer

Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer -2f(1) = Answer

What values of x will make the statement x+5=3 or x2=9. Answers:

x = Answer

or

(x = Answer

and x = Answer

) <--- For this, write the least value first.

What is the slope of the line through (3,9) and (x,y) for y=x2 and x=2.97? x=3.001? x=3+h? What happens to this last slope when h is very small (close to 0)? Round-off your answers to 2 decimal places, whenever possible. Answers: (Write the letter first before the number, whenever possible.) Slope at x=2.97 = Answer Slope at x=3.001 = Answer Slope at x=3+h = Answer Slope when h is close to 0 = Answer What is the slope of the line through (2,4) and (x,y) for y = x2 + x - 2 and x=1.99? x=2.004? x=2+h. What happens to this last slope when h is very small? Answers: when x=1.99: m = Answer

Round-off your answer to 2 decimal places.

when x=2.004: m = Answer

Round-off your answers to 3 decimal places.

when x=2+h:m = Answer when h approaches 0: m = Answer What is the slope of the line through (-1,-2) and (x,y) for y = x2 + 2x + 1 and x=-0.90? x=-1.05? x=h-1? What happens to this last slope when h is very small? Round-off your answers to 2 decimal places whenever possible. Use the ^ symbol to express the exponent of a variable, i.e. x^2 (x squared). Do not use spaces on your answers Answers: when x=-0.90: m = Answer when x=-1.05: m = Answer when x=h-1: m = Answer

/h

when h approaches 0: m = Answer The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=0 to t= 20 sec?

(b) What was the average velocity from t=10 to t=30 sec? (c) About how fast was the car traveling at t=15 sec? Answers: (a) V = Answer

ft/sec

(b) V = Answer

ft/sec

(c) V = Answer

ft/sec

Define A(x) to be the area bounded by x and y axes, the line y=x+1, and the vertical line at x. (a) Evaluate A(2) and A(3) (b) What area would A(3) - A(1) represent? Answers: (a) A(2) = Answer

square units

(b) A(3) - A(1) = Answer

A(3) = Answer

square units

square units

Which of the following are negation of the statement: f(x) and g(x) are polynomials. c. f(x) and g(x) are not polynomials d. f(x) or g(x) is a polynomial

The graph shows the population growth of bacteria on a petri plate. If at t=10 days, the population grows to 4600 bacteria, find the rate of population growth from t=9 to t= 10 days? Answer: rate of growth = Answer Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3. Answer: If x = - Answer

and x = Answer

then x2 + x - 6 is not equal to 0

(NOT SURE)

Given g(t) = t+5t−1t+5t−1, evaluate: (a) g(5) and (b) g(2s - 5) (a) g(5) = 5/2

(b) g(2s-5) = s/s-3 Find the slope of the line through (-5,3) and (x+1, x-2).

M=ANSWER? Try 1 Let f(x)=-1-x-2x2, evaluate Which graph represents the function =

Evaluate limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3

ANSWER= 108 / 7 Evaluate limx→0cos2x−1cosx−1limx→0cos2x−1cosx−1

ANSWER= 4 Every vertical line on the Cartesian plane intersects the x-axis.

=TRUE Write the contrapositive of the statement: I feel good when I jog. Answer: When I don't jog, I feel

Answer: Bad Evaluate limx→35x2−8x−13x2−5

=2 The sum of two prime numbers is a prime.

=False Write the negation of the statement: 8 is a prime number.

Answer: 8 is

= not a prime number

Evaluate limx→103x−5−−−−−√5

=5 Evaluate limx→43−x+5−−−−√x−4

=1 / 6 Which values of x will make the statement x+5=3 or x2=9 true?

=-2 or (3 and -3) Evaluate limx→1x13−1x14−1

=4 / 3

Quiz 6 Use the function f defined by the graph shown to determine the following limits: (a) limx→1+f(x)limx→1+f(x) (b) limx→1−f(x) Answers: A= B=

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1). f(-3) = -1 f(-1) = 1 f(0) = 0 f(1) = 1 Refer to the figure. Which of the following represents the graph drawn in red? =g(x)-1

If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function. =True Let f(x) = 1-(x-1)2 evaluate (a)f(2)f(3)

and (b)f(23)

(a) = (b) = Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). f(-1) = -1 -2f(1) = 6 The slope of the line through (5,15) and (x+8, x2-2x) is =x-5 Which of the following is the contrapositive for the statement: If your car is properly tuned, it will get at least 24 miles per gallon.

=If your car will not get at least 24 miles per gallon, then it is not properly tuned. Which of the following will make the statement x2+3 > 1 true?

=x is less than or equal to -1 From the graph shown, find: a. f(-1) b. f(0) c. 3f(2) d. the value of x that corresponds to f(x)=0 a. f(-1) =2 b. f(0) =1 c. 3f(2) = 2 (not sure) d. x = 0 (not sure) Let f(x) = 2-x2, evaluate (a) f(x+1) and (b) f(x)+f(1). (a) f(x=1) = -x2- 2x+1 (b) f(x) + f(1) = -x2+ 3 Find the slope of the line through (0,0) and (x-1, x2-1).

M= x+1

Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1). Answers: (a) 1

–x

(b) 1- x

(c) -4 x2 + 8x-3 Which graph corresponds to f(x) = √x?

From the figure shown, find the values of f(2), f(-1) and f(0). f(2) =

5

f(-1) = 2 f(0) = 1 Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any. (a) 3x-10 (b) 3x-6 (c) -1/5 (d) -3

Let A = {1,2,3,4,5}, B = {0,2,4,6}, and C = {-2,-1,0,1,2,3}. Which of the values of x will satisfy each statement? = x is not in B and x is in C

Let f(x)=-1-x-2x2, evaluate f(x+h)−f(x)hf(x+h)−f(x)h Factor out the negative sign for the final answer, if any. Answer: -(4x+2h+1) Find the slope of the line through (-3-1) and (x+3, y+1). =?? x-5/x+6 (try)

Which graph represents the function f(x) = {2 if x ≤ -1} {x2 if x > -1}

If a and b are real numbers, then (a+b)2 = a2+b2.

=False

Which graph represents the function

f(x) = {2 if x ≤ -1} {x2 if x > -1}

Given f(x) = 2x + 3. Evaluate (f°f)(x). Sample text answer: 3x^2+6x-7. Do not use space between the number, letter and symbol.

=4x+9 A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. Given that variable x shall be the length of one edge of the square cu from each corner of the sheet of cardboard, what will be the dimensions of the box with largest volume? (Note: Answer should be in decimal form and up to two decimal places only)

x ≈ 0.57 ft, so Length= 2.86 ft

Width = 1.86ft Height = 0.57 ft CALCULUS 1 By: Grace Carticiano & Francheska Cuison QUIZZES Quiz 3

The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=10 to t=30 seconds? (b) What was the average velocity of the car from t=20 to t=25 seconds? a) average velocity = Answer (b) average velocity = Answer

feet/second feet/second

The figure shows the temperature during a day in a place. How fast is the temperature changing from 1:00 P.M. to 7:00 P.M.? Round-off your answer to 2 decimal places. Answer: Answer

0

F/hour

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1) Answers: (a) A(2.5) = Answer (b) A(4) - A(1) = Answer

square units square units

For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o f(x). Note: For exponential answer, express it like x^3 for x cubed. Use lowercase letters, and do not put spaces in your answer. Answer: f o g(x) = Answer g o f(x) = Answer

3x^2+1 9x^2-12x+5

Refer to the figure. Which of the following represents the graph drawn in red? Select one: a. | g(x) | b. g(x-1) c. [ g(x) ] d. g(x)-1

An enrollment slip indicates a specific down payment based from the number of units enrolled by a student as follows: for number of units from 1 to 9, down payment is Php 5000; for number of units from 10 to 15, down payment is Php 10,000; and a down payment of Php 15,000 for units from 16 to 21. Which of the multiline functions define E(d), the down payment due on specific number of units enrolled. Unit is of integer type.

Evaluate f(3), g(-1), and h(4). Answer: f(3) = Answer g(-1) = Answer h(4) = Answer After evaluating g(-4), g(-1) and g(3), choose which graph represents the given conditions.

Answer:

A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function for T(x), the state income tax due on earnings of x dollars.

Answer:

Given g(x) = (x+3)/(x-1). Evaluate g(5) and g(2n+1). Note that fractional answers must be expressed like -5/6, and answers with exponents like (x^2-1)/(x+3). Use lower case letters.and do not use spaces in your answers. Answer: g(5) =Answer

and g(2n+1) =Answer

A function f is given by f(7-11x) = 3x3 - 10x. Evaluate f(-4). Answer: f(-4) =Answer A FUNCTION assigns a unique output element in the range to each input element from the domain.

For y=f(x), x is the domain, and y is the range

Given f(x) = x3 - 4x2 +2, f(2) when evaluated is -6.

Which of the following figures represents the graph of a function?

Select one: a. Figures 1 and 2 b. Figure 2 c. Figure 1 d. Figure 3 e. All of the figures f. Figures 1 and 3

Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)). Note: Do not use spaces in your answers. Answer: (Write your answer in this format: x+A+1) f(g(x)) =Answer g(f(x)) =Answer A =Answer

For f(x) = |9-x| and g(x) = sqrt(x-1). Evaluate fog(1). Answer: f(g(1) =Answer

Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any. Answers: (a) Answer (b) Answer (c) Answer (d) Answer

Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = Answer

From the figure shown, find the values of f(2), f(-1) and f(0). Answers: f(2) =Answer f(-1) =Answer f(0) =Answer

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1). Answers: f(-3) = Answer f(-1) = Answer f(0) = Answer f(1) = Answer

Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer -2f(1) = Answer

What values of x will make the statement x+5=3 or x2=9. Answers:

x = Answer

or

(x = Answer

and x = Answer

) <--- For this, write the least value first.

What is the slope of the line through (3,9) and (x,y) for y=x2 and x=2.97? x=3.001? x=3+h? What happens to this last slope when h is very small (close to 0)? Round-off your answers to 2 decimal places, whenever possible. Answers: (Write the letter first before the number, whenever possible.) Slope at x=2.97 = Answer Slope at x=3.001 = Answer Slope at x=3+h = Answer Slope when h is close to 0 = Answer What is the slope of the line through (2,4) and (x,y) for y = x2 + x - 2 and x=1.99? x=2.004? x=2+h. What happens to this last slope when h is very small? Answers: when x=1.99: m = Answer

Round-off your answer to 2 decimal places.

when x=2.004: m = Answer

Round-off your answers to 3 decimal places.

when x=2+h:m = Answer when h approaches 0: m = Answer What is the slope of the line through (-1,-2) and (x,y) for y = x2 + 2x + 1 and x=-0.90? x=-1.05? x=h-1? What happens to this last slope when h is very small? Round-off your answers to 2 decimal places whenever possible. Use the ^ symbol to express the exponent of a variable, i.e. x^2 (x squared). Do not use spaces on your answers Answers: when x=-0.90: m = Answer when x=-1.05: m = Answer when x=h-1: m = Answer

/h

when h approaches 0: m = Answer The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=0 to t= 20 sec?

(b) What was the average velocity from t=10 to t=30 sec? (c) About how fast was the car traveling at t=15 sec? Answers: (a) V = Answer

ft/sec

(b) V = Answer

ft/sec

(c) V = Answer

ft/sec

Define A(x) to be the area bounded by x and y axes, the line y=x+1, and the vertical line at x. (a) Evaluate A(2) and A(3) (b) What area would A(3) - A(1) represent? Answers: (a) A(2) = Answer

square units

(b) A(3) - A(1) = Answer

A(3) = Answer

square units

square units

The graph shows the population growth of bacteria on a petri plate. If at t=10 days, the population grows to 4600 bacteria, find the rate of population growth from t=9 to t= 10 days? Answer: rate of growth = Answer Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3. Answer: If x = - Answer

and x = Answer

then x2 + x - 6 is not equal to 0

QUIZ 4 The slope of the line through (5,15) and (x+8, x2-2x) isAnswer

Given g(t) = t+5t−1t+5t−1, evaluate: (a) g(5) and (b) g(2s - 5) Answer: (a) g(5) = Answer

.

(b) g(2s-5) = Answer

Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer -2f(1) = Answer

Which of the following are negation of the statement: f(x) and g(x) are polynomials. Select one or more: a. f(x) or g(x) is a polynomial b. g(x) is a polynomial c. f(x) and g(x) are not polynomials d. f(x) is a polynomial Find the slope of the line through (-5,3) and (x+1, x-2). Answer: m = Answer

QUIZ 5 limx→0cos2x−1cosx−1limx→0cos2x−1cosx−1

Evaluate Answer: 4

Write the contrapositive of the statement: I feel good when I jog. Answer: When I don't jog, I feel Answer: Bad

Evaluate

limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3

Answer: Answer

/ Answer

Write the negation of the statement: 8 is a prime number. Answer: 8 is Answer: not a prime number

Evaluate

limx→1x13−1x14−1limx→1x13−1x14−1

Answer: Answer

Evaluate

/ Answer

limx→103x−5−−−−−√5limx→103x−55

Answer: Answer

Every vertical line on the Cartesian plane intersects the x-axis. Select one: True False

Evaluate

limx→43−x+5−−−−√x−4limx→43−x+5x−4

Answer: - Answer Evaluate

/ Answer

limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5

Answer: Answer Which values of x will make the statement x+5=3 or x2=9 true? Select one:

a. (-2 and 3) or -3 b. -2 or (3 and -3) c. -2 and (3 or -3) d. (-2 or 3) and -3 Clear my choice

The sum of two prime numbers is a prime. False

QUIZ 6 Use the function h defined by the graph shown to determine the following limits:

limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3) (a)

Answers: (a) Answer (b) Answer

At which values of x is the function discontinuous?Answers:

f(x)=x2+x−6x−2f(x)=x2+x−6x−2continuous and

continuous at x = Answer discontinuous at x = Answer Use the function h defined by the graph below to determine the following limits:

limx→2x+h(x)limx→2x+h(x) (b) limx→3h(x2) (a)

Answers: (a) Answer (b) Answer

Use the graph below to determine the right-hand limit of the function f(x) at: (a) x=-2 (b) x=10 Answers: (a) Answer (b) Answer Use the functions f and g defined by the graphs as shown to determine the following limits:

limx→1(f(x)xg(x))limx→1(f(x)xg(x)) (b) limx→1f(g(x)) (a)

Answers: (a) Answer (b) Answer Use the function h defined by the graph below to determine the following limits:

limx→2(xlimx→2(x . h(x−1))h(x−1)) (b) limx→0h(3+x)−h(3)h(x) (a)

Answers: (a) Answer (b) Answer At which values of x is the function from the graph shown continuous? State the answers from the least to the highest, if there would be more than one. Answer: x = Answer Use the function f defined by the graph shown to determine the following limits:

limx→1+f(x)limx→1+f(x) (b) limx→1−f(x) (a)

Answers:

(a) Answer (b) Answer Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x2 - 2 on [0,3] Answer: Answer Use the function h defined by the graph as shown to determine the following limits:

limx→2h(2x−2)limx→2h(2x−2) (b) limx→2h(1+x) (a)

Answers: (a) Answer (b) Answer

MIDTERM EXAM If a and b are real numbers, then (a+b)2 = a2+b2. Select one: True False Which of the following is the contrapositive for the statement: If your car is properly tuned, it will get at least 24 miles per gallon. Select one: a. If your car will not get at least 24 miles per gallon, then it is not properly tuned. b. If your car is properly tuned, then it will not get at least 24 miles per gallon. c. If your car is not properly tuned, it will not get at least 24 miles per gallon. If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function. Select one:

True False Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1). Answers: (a) Answer

- Answer

2

(b) Answer

- Answer

2

(c) Answer

x2 + Answer

Which of the following will make the statement x2+3 > 1 true? Select one: a. x = -1 b. x is greater than or equal to -1(TRY) c. x > -1 d. x is less than or equal to -1

Let f(x) = 1-(x-1)2 evaluate Answers:

(a)f(2)f(3) and (b)f(23)(a)f(2)f(3) and (b)f(23)

(a) Answer (b) Answer

Find the slope of the line through (-3-1) and (x+3, y+1). Answer: Answer

From the graph shown, find: a. f(-1) b. f(0) c. 3f(2)

d. the value of x that corresponds to f(x)=0 Answers: a. f(-1) = Answer b. f(0) = Answer c. 3f(2) = Answer d. x = Answer Let A = {1,2,3,4,5}, B = {0,2,4,6}, and C = {-2,-1,0,1,2,3}. Which of the values of x will satisfy each statement? Select one: a. x is in A or x is in C b. x is in A and x is in B c. x is not in B and x is in C Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = 1 Which graph corresponds to f(x) = √x?

Which graph represents the function f(x) = {2 if x ≤ -1} {x2 if x > -1}

FINALS EXAM Use linear equation to estimate e0.06. Choose a value of 'a' to produce a small error. Note: Answers should be in decimal form. Up to two decimal places only.

e0.06 = Answer Determine all the critical points for the function.

f(x)=xex2

Determine whether the graph is continuous or not continuous.

Answer: Not Continuous

Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x5 - 3x on [1,3] Answer: There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?

x = Answer

P = Answer

additional trees

apples

Use chain rule to calculate dydxdydx of y=sin(4x3+3x+1)y=sin(4x3+3x+1) Select one: a. dydx=(12x2−3)cos(4x3+3x−1)dydx=(12x2−3)cos(4x3+3x−1)

b. dydx=(12x2+3)cos(4x3+3x+1)dydx=(12x2+3)cos(4x3+3x+1)

c. dydx=(12x2+3)cos(4x3+3x−1)dydx=(12x2+3)cos(4x3+3x−1)

d. dydx=(12x2−3)cos)4x3+3x+1)

Find a value for B so that the line y = 10x – B, goes through the point (5,-5). Answer: B = Answer For all positive real numbers a and b, if a > b, then a2 > b2

Answer: TRUE Determine whether the graph is continuous or not continuous.

Answer: Continuous Find the equation of the line tangent to the circle x2 + y2 = 25 at point (3,4). Use the general equation of the line for your final answer. Answer: 3x + Answer

y - Answer

=0

You are standing at the edge of a slow-moving river which is one mile wide and wish to return to your campground on the opposite side of the river. You can swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the campground, which is one mile from the point directly across the river from where you start your swim. What route will take the least amount of time? (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer

mi.

Shortest possible time: T ≈ Answer

hr.

Determine whether the graph is continuous or not continuous.

Answer: Not Continuous Question 14 Not yet answered Marked out of 1.00

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Question text Find an equation of the line tangent to the graph of Select one: a. y=76x−136y=76x−136

b. y=76x+136y=76x+136

c. y=136x−76y=136x−76

d. y=136x+76y=136x+76

x2+(y−x)3=9x2+(y−x)3=9 at x=1

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Question text Use linear approximations to estimate 1–√46146. Choose a value of "a" to produce a small error. Note: Answers should be in decimal form. Up to two decimal places only.

1–√46=f(146)≈L(146)146=f(146)≈L(146) = Answer Question 16 Not yet answered

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Question text Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.

(Note: Answers should be in decimal form. Up to two decimal places only)

r ≈ Answer h ≈ Answer

V ≈ Answer

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Question text Find the slope and concavity of the graph pf x2y+y4=4+2xx2y+y4=4+2x at the point (-1,1) Select one: a. Slope = 2525, Concavity = downward

b. Slope = 5454, Concavity = downward

c. Slope = 4545, Concavity = downward

d. Slope = 4545, Concavity = upward

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Question text A container in the shape of a right circular cylinder with no top has surface area 3 ft.2 What height h and base radius r will maximize the volume of the cylinder? (Note: answers should be in decimal form. Up to two decimal places only)

r = Answer

ft.

h = Answer

ft.

V = Answer

ft3

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Question text If a and b are real numbers then (a + b)2 = a2 + b2. Select one: True False

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for cos2x+cos2y=cos(2x+2y)cos2x+cos2y=cos(2x+2y) Select one: a. y1=cosxsinx+sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx+sin(2x+2y)sin(2x+2y)−cosysiny

b. y1=cosxsinx−sin(2x+2y)sin(2x+2y)+cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)+cosysiny

c. y1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysiny

d. y1=cosxsinx+sin(2x+2y)sin(2x+2y)+cosysinyy1=cosxsinx+sin(2x+2y)sin(2x+2y)+cosysiny

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Find a linear approximation to h(t)=t4−6t3+3t−7h(t)=t4−6t3+3t−7 at t=−3t=−3. (Note: Complete the linear approximation by filling in the missing numbers. Answers should be in decimal form. Up to two decimal places only)

L(t) = Answer

- Answer

(t + 3) = Answer

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Question text Find the local extreme values of the given function:

f(x)=x4−6x2f(x)=x4−6x2 Select one: a. Local minimum: (1.73, -9) Local maximum: (-1.73, -9) b. Local minimum: (1.73, 9) Local maximum: (-1.73, 9) c. Local minimum: (-1.73, 9) Local maximum: (1.73, 9) d. Local minimum: (-1.73, -9) Local maximum:(1.73, -9) Clear my choice Question 23 Not yet answered Marked out of 1.00

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t - Answer

Question text Use chain rule to calculate dydxdydx of y = tan (e3x√)(e3x) Select one: a.

dydx=−sec2(e3x−−√)2e3x√33x−−√dydx=−sec2(e3x)2e3x33x b.

dydx=sec2(e3x−−√)2e3x√33x−−√dydx=sec2(e3x)2e3x33x c.

dydx=sec2(e3x−−√)3e3x√23x√dydx=sec2(e3x)3e3x23x d. dydx

=−sec2(e3x−−√)3e3x√23x−−√dydx=−sec2(e3x)3e3x23x

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Question text Use chain rule to calculate dydxdydx of y=cos4(7x3)y=cos4(7x3) Select one: a. dydx=84x2cos3(7x3)sin(7x3)dydx=84x2cos3(7x3)sin(7x3)

b. dydx=−84x2cos3(7x3)+sin(7x3)dydx=−84x2cos3(7x3)+sin(7x3)

c. dydx=−84x2cos3(7x3)sin(7x3)dydx=−84x2cos3(7x3)sin(7x3)

d. dydx=84x2cos3(7x3)+sin(7x3)dydx=84x2cos3(7x3)+sin(7x3)

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Consider the function below. (\Large \lim_{x \rightarrow 3} (2x + 1) = 7 \)

What values of x guarantee that f(x) = 2x + 1 is within 0.04 units of 7? If x is within Answer 7. Question 26 Not yet answered Marked out of 3.00

units of 3, then f(x) is within 0.04 units of

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Question text Find the point of intersection and the angle between x - y = 32 and 3x - 8y = 6. Answers: Point of Intersection = ( Answer Angle of Intersection = Answer

, Answer 0

)

(round-off to 2 decimal places)

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Question text If f(x) and g(x) are linear functions then f(x)g(x) is a linear function. Select one: True False Question 28 Not yet answered Marked out of 1.00

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Question text Use the function h defined by the graph below to determine the following limits:

limx→2(xlimx→2(x . h(x−1))h(x−1)) (b) limx→0h(3+x)−h(3)h(x)limx→0h(3+x)−h(3)h(x) (a)

Answers: (a) Answer (b) Answer Question 29 Not yet answered Marked out of 1.00

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Question text Determine all the critical points for the function.

f(x)=x2ln(3x)+6f(x)=x2ln(3x)+6 Select one: a. 0 b. 0.20 c. no correct answer d. 0.50 Clear my choice Question 30 Not yet answered Marked out of 1.00

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Question text Which of the following equations is the line perpendicular to 2x – 3y = 9? Select one: a. 3x + 2y =11 b. 3x – 2y = 10 c. 3x + 2y =10 d. 2x – 3y =11 Clear my choice Question 32 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 33 Not yet answered Marked out of 1.00

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Question text Given a function f, an interval [a,b] and a value V. Find a value c in the interval so that f(c)=V. Apply the Intermediate Value Theorem. NOTE: Round-off your answers to 2 decimal places, stating from the least to the highest, if there would be more than one. For positive answers, do not state the + sign anymore. For answers less than 1, precede them with 0, example 0.11

f(x)=x2f(x)=x2 on [0,3], V = 2 (b) f(x)=sinx on [0,π2],V=12f(x)=sinx on [0,π2],V=12 (a)

Answers: (a) c = Answer (b) c = Answer

; c = Answer

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Question text Evaluate

limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3

Answer: Answer

/ Answer

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Question text Find an equation of the line tangent to the graph of y=x2+sinπ2xy=x2+sinπ2x at x = -1 Select one: a. y = 2x - 2 b. y = -2x - 2 c. y = 2x + 2 d. y = -2x + 2 Clear my choice Question 36 Not yet answered Marked out of 1.00

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Question text Use implicit differentiation to finddydxdydx

exy=2yexy=2y Select one: a.

y1=yexy2−exxyy1=yexy2−exxy

b.

y1=yexy2−xexyy1=yexy2−xexy

c.

y1=yexy2+xexyy1=yexy2+xexy

d.

y1=yexy2+exxyy1=yexy2+exxy Clear my choice

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Question text

Answers: (a) Answer (b) Answer (c) Answer Question 38 Not yet answered Marked out of 2.00

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Question text

(Note: Answers should be in decimal form. Up to two decimal places only)

x = Answer Smallest sum:

S = Answer Question 39 Not yet answered Marked out of 1.00

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Question text What is the slope of the line through (-1,-2) and (x,y) for y = x2 + x – 2 and x=-0.98. Round-off your answer to 2 decimal places whenever possible. Answer: slope = Answer Question 40 Not yet answered Marked out of 2.00

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Question text Which of the following equations is the line perpendicular to 4y – 7x = 5?

Select one: a. 4y – 7x + 9 = 0 b. 4x + 7y – 18 = 0 c. 4x + 7y + 18 = 0 d. 7x – 4y + 9 = 0 Clear my choice Question 41 Not yet answered Marked out of 1.00

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Consider the function below.

limx→31+x−−−−√=2limx→31+x=2 What values of x guarantee that

f(x)=1+x−−−−√f(x)=1+x is within 0.0002 units of 2?

If x is within Answer of 2. Question 42 Not yet answered Marked out of 3.00

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units of 3, then f(x) is within 0.0002 units

Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only: 1. Write the equation of the line that represents the linear approximation to the function below at a given point a. f(x) = ln(1 + x); a = 0; f(0.9) y = L(x) = Answer 2. Use linear approximation to estimate the given function value. f(0.9) = Answer 3. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact Percent error: Answer

%

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Question text The slope of the line from point U(5,13) and the point V(x+1, x2-3) isAnswer Question 44 Not yet answered Marked out of 1.00

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Question text Use chain rule to calculate dydxdydx of

y=x2sec(5x)y=x2sec(5x) Select one:

.

a. dydx

=−2xsec(5x)+5x2sec(5x)tan(5x)dydx=−2xsec(5x)+5x2sec(5x)tan(5x)

b. dydx

c. dydx

=2xsec(−5x)+5x2sec(5x)tan(5x)dydx=2xsec(−5x)+5x2sec(5x)tan(5x)

=2xsec(5x)−5x2sec(5x)tan(5x)dydx=2xsec(5x)−5x2sec(5x)tan(5x)

d. dydx

=2xsec(5x)+5x2sec(5x)tan(5x)dydx=2xsec(5x)+5x2sec(5x)tan(5x)

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Question text Let f(x) = (x-1)2 and define S(x) to be the slope of the line through the point (0,0) and (x,f(x)). Evaluate S(6). Answer: S(6) =Answer (Use fractional answer when possible, say 12/13. Do not use space between symbol and number.) Question 46 Not yet answered Marked out of 3.00

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Question text

(Note: Answers should be in decimal form only. Up to two decimal places}

x ≈ Answer

ft.

y ≈ Answer

ft.

L ≈ Answer

ft.

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Question text Evaluate

limx→0(x+1)3−1xlimx→0(x+1)3−1x

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Fill in the missing the numbers to find the correct answer/s: Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.

P = xy

2

Answers:

x = Answer y = Answer P = Answer Question 49 Not yet answered Marked out of 1.00

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Question text If f(x) and g(x) are linear functions, then f(x) + g(x) is a linear function. Select one: True False Question 50 Not yet answered Marked out of 1.00

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Use Newton's Method to find the root of 2x2+5=ex2x2+5=ex accurate to six decimal places in the interval [3,4]. (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer Question 51 Not yet answered Marked out of 2.00

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Question text

(Note: Answer should be in decimal form. Up to two decimal places only)

x ≈ Answer

ft.

θ = Answer

degrees.

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Question text A hotel charges Php1,500 per night for a room during the tourist season from June 1 through September 15, and Php1,200 per night otherwise. Define a multiline function which describes these rates. f(x) is the cost for one night on date x . Choose from the options. Select one:

a.

b.

c. Clear my choice Question 53 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 54 Not yet answered Marked out of 1.00

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Question text

Consider the function below.

limx→24x−3=5limx→24x−3=5 What values of x guarantee that f(x) = 4x - 3 is within 1 unit of 5? Select one: a. If x is within 2.25 units distance of 2, then f(x) is within 1 unit of 5. b. If x is within 1.75 units distance of 2, then f(x) is within 1 unit of 5. c. If x is within 0.25 unit distance of 2, then f(x) is within 1 unit of 5. d. If x is within 2 units distance of 2, then f(x) is within 1 unit of 5. Clear my choice

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Question text

(Note: Answers should be in decimal form only. Up to two decimal places only)

x = Answer y = Answer

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Consider the function below.

limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5? Select one: a. If x is within 0.98 unit distance of 1, then f(x) is within 0.05 unit of 5. b. If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5. c. If x is within 1.02 units distance of 1, then f(x) is within 0.05 unit of 5. d. If x is within 1 unit distance of 1, then f(x) is within 0.05 unit of 5. Clear my choice Question 57 Not yet answered Marked out of 1.00

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Question text Determine all the critical points for the function

y=6x−4cos(3x)y=6x−4cos(3x) x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,... x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,...

Select one:

a. 1.2217; 1.9199 b. 1.2217; 0.9199 c. 1.7991; 1.2217 d. 1.1991; 1.7122 Clear my choice Question 58 Not yet answered Marked out of 1.00

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for x−y3y+x2 Select one: a. y1=1−y+3x2−4x3y2+x−2y1=1−y+3x2−4x3y2+x−2

b. y1=1−y−3x2−4x3y2−x+2y1=1−y−3x2−4x3y2−x+2

c. y1=1−y−3x2−4x3y2+x+2y1=1−y−3x2−4x3y2+x+2

d. y1=1−y+3x2−4x3y2+x+2y1=1−y+3x2−4x3y2+x+2

Clear my choice Question 59 Not yet answered Marked out of 1.00

=x+2x−y3y+x2=x+2

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Question text Evaluate

limx→0(x+5)2−25xlimx→0(x+5)2−25x

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Question text Evaluate

limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5

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Question text Do the following. Type your answer on the space/s provided. Up to two decimal places only. 1. Write the equation of the line that represents the linear approximation to the function below at the given point a.

f(x)=e2;a=0;f(0.05)f(x)=e2;a=0;f(0.05)

f(a) = Answer

2. Use the linear approximation to estimate the given function value.

f(0.05) ≈ L (0.05) = Answer 3. Compute the percent error in your approximation.

Percent error ≈ Answer

%

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Given f(x) = 2x + 3 and g(x) = x2. Evaluate not use space between the number, letter and symbol.

. Sample text answer: 3x^2+6x-7. Do

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Question text Use Newton's Method to determine x2x2 for f(x)=xcos(x)−x2f(x)=xcos(x)−x2 if x0=1x0=1 (Note: Answers should be in decimal form. Up to two decimal places only.)

x2 = Answer Question 64 Not yet answered Marked out of 1.00

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for (x−y)2=x+y−1(x−y)2=x+y−1 Select one: a. y1=2y−2x+12y−2x−1y1=2y−2x+12y−2x−1

b. y1=2y−2x+12y+2x−1y1=2y−2x+12y+2x−1

c. y1=2y+2x−12y+2x+1y1=2y+2x−12y+2x+1

d. y1=2y+2x−12y−2x+1y1=2y+2x−12y−2x+1

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Question text Use chain rule to calculate dydxdydx of

y=e−x2y=e−x2 Select one:

a. dydx

=2x−x2dydx=2x−x2

b. dydx

c. dydx

=−2x−x2dydx=−2x−x2

=2xx2dydx=2xx2

d. dydx

=−2xx2dydx=−2xx2

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Question text Locate the critical points of the following functions. Then use the second derivative test to determine whether they correspond to local minima or local maxima or whether the test is inconclusive.

p(x)=x−4x2+20p(x)=x−4x2+20 Select one: a. Critical points: (1, -1/4) and (2, -1/20) Local minimum: x = -2 Local maximum: x = 5

b. Critical points: (2, -3/4) and (10, -1/20) Local minimum: x = -20 Local maximum: x = 1 c. Critical points: (2, -1/4) and (10, -1/2) Local minimum: x = 2 Local maximum: x = 10 d. Critical points: (2, -1/4) and (10, -1/20) Local minimum: x = -2 Local maximum: x = 10 Clear my choice Question 67 Not yet answered Marked out of 1.00

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Question text Use Newton's Method to find the root of x4−5x3+9x+3=0x4−5x3+9x+3=0 accurate to six decimal places in the interval [4,6]. (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer Question 68 Not yet answered Marked out of 1.00

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Identify the absolute extrema and relative extrama for the following function.

f(x)=x3f(x)=x3 on [-2,2] Select one: a. The function has an absolute maximum of 8 at x = 0 and absolute minimum of -8 at x = -1. The function has a no relative extrema. b. The function has an absolute maximum of -8 at x = 2 and absolute minimum of 8 at x = -2. The function has no relative extrema. c. The function has an absolute maximum of 8 at x = 2 and absolute minimum of -8 at x = -2. The function has no relative extrema. d. The function has an absolute maximum of 8 at x = -2 and absolute minimum of -8 at x = 2. The function has a relative minimum of (0,0) and no relative maxmum. Clear my choice Question 69 Not yet answered Marked out of 1.00

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Question text Use the functions f and g defined by the graphs as shown to determine the following limits:

limx→1f(x)+g(x)limx→1f(x)+g(x) (b) limx→2f(x)g(x)limx→2f(x)g(x) (a)

Answers: (a) Answer (b) Answer Question 70 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 71 Not yet answered Marked out of 1.00

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Question text Use implicit differentiation to find dydxdydx

(xy+1)3=x−y2+8(xy+1)3=x−y2+8 Select one: a.

y1=1−3y(xy+1)23x(xy+1)2+2yy1=1−3y(xy+1)23x(xy+1)2+2y

b.

y1=1+3y(xy+1)23x(xy+1)2−2yy1=1+3y(xy+1)23x(xy+1)2−2y

c.

y1=2y+2x−12y−2x+1y1=2y+2x−12y−2x+1

d.

y1=1+3y(xy+1)23x(xy+1)2+2yy1=1+3y(xy+1)23x(xy+1)2+2y Clear my choice

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Question text Evaluate

limx→7x−3−−−−√limx→7x−3

Answer: Answer

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Question text Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen? (Note: Answers should be in decimal form. Up to two decimal places only)

x = Answer y = Answer A = Answer

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ft. ft. ft2

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Question text For the function

f(x)=x(x2+1)2f(x)=x(x2+1)2 on [-2,2] Find the critical points and the absolute extreme values of f on the given interval. Select one: a. x=±23−−√x=±23 as the critical points absolute maximum value of f: −33√16−3316 absolute minimum value of f: 33√163316

b. x=13−−√x=13 as the critical points absolute maximum value of f: −33√16−3316 absolute minimum value of f: −33√16−3316

c. x=±13−−√x=±13 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:33√163316

d. x=±12−−√x=±12 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:: 33√163316

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for y=x2y3+x3y2y=x2y3+x3y2 Select one: a. y1=2xy3+3x2y21+3x2y2+2x3yy1=2xy3+3x2y21+3x2y2+2x3y

b. y1=2xy3+3x2y21−3x2y2+2x3yy1=2xy3+3x2y21−3x2y2+2x3y

c. y1=2xy3+3x2y21−3x2y2−2x3yy1=2xy3+3x2y21−3x2y2−2x3y

d. y1=2xy3+3x2y21+3x2y2−2x3yy1=2xy3+3x2y21+3x2y2−2x3y

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Question text

Consider the function below.

limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5?

Select one: a. If x is within 1.02 units distance of 1, then f(x) is within 0.05 unit of 5. b. If x is within 0.98 unit distance of 1, then f(x) is within 0.05 unit of 5. c. If x is within 1 unit distance of 1, then f(x) is within 0.05 unit of 5. d. If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5. Clear my choice Question 77 Not yet answered Marked out of 3.00

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Question text An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions will result in a box with the largest possible volume?

Answers:

x = Answer

ft.

y = Answer

ft.

V = Answer

ft.3

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Question text Write the negation for the statement: All quadratic equations have solutions. Answer: Answer

all quadratic equations Answer

solutions.

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Question text Use the function h defined by the graph shown to determine the following limits:

limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3)limx→0h(3+x)−h(3) (a)

Answers: (a) Answer (b) Answer

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Question text Use implicit differentiation to find dydxdydx,

x3=x+yx−yx3=x+yx−y Select one: a.

y1=3x2(x−y)2+2y2xy1=3x2(x−y)2+2y2x

b.

y1=3x2(x−y)2−2y2xy1=3x2(x−y)2−2y2x

c.

y1=3x2(x+y)2+2y2xy1=3x2(x+y)2+2y2x

d.

y1=3x2(x+y)2−2y2xy1=3x2(x+y)2−2y2x Clear my choice

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Question text

Find the point of intersection and the angle between y = 4 - 2x and x - y = -1. Answers: Point of Intersection = ( Answer Angle of Intersection = Answer

, Answer 0

)

(round-off to 2 decimal places)

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Question text Find a linear approximation of f(x)=3xe2x−10f(x)=3xe2x−10 at x = 5. (Note: Fill in the missing numbers to get the get the correct answer. Answers should be in decimal form. Up to two decimal places only.) L(x) = Answer

+ Answer

(x - 5) = Answer

x + Answer

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 84 Not yet answered Marked out of 3.00

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Question text Find the point of intersection and the angle between 2x - 3y = 3 and 4x - 2y = 10. Answers: Point of Intersection = ( Answer Angle of Intersection = Answer Question 85 Not yet answered Marked out of 3.00

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, Answer 0

)

(round-off to 2 decimal places)

Question text Which of the following is the appropriate multiline function for the graph shown?

Select one:

a.

b. c. Last option napicture Clear my choice Question 86 Not yet answered Marked out of 3.00

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Question text Consider a rectangle of perimeter 12 inches. Form a cylinder by revolving this rectangle about one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume? (Note: Answer should be in decimal form. Up to two decimal places only)

r = Answer

ft

h = Answer

ft

V ≈ Answer

ft3

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Question text Evaluate

limx→43−x+5−−−−√x−4limx→43−x+5x−4

Answer: - Answer

/ Answer

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Question text

Use chain rule to calculate dydxdydx of

y=(5x2+11x)20y=(5x2+11x)20 Select one: a. dydx=(−20)(5x2+11x)19(10x+11)dydx=(−20)(5x2+11x)19(10x+11)

b. dydx=(20)(5x2+11x)19(10x+11)dydx=(20)(5x2+11x)19(10x+11)

c. dydx=(20)(5x2+11x)19(10x−11)dydx=(20)(5x2+11x)19(10x−11)

d. dydx=(−20)(5x2+11x)19(10x−11)dydx=(−20)(5x2+11x)19(10x−11)

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Question text Determine whether the graph is continuous or not continuous.

Select one:

a. Not Continuous b. Continuous Clear my choice Question 90 Not yet answered Marked out of 1.00

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Question text Evaluate

limx→103x−5−−−−−√5limx→103x−55

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Question text Which of the following are integer values of x that will make the statement x>4 and x<9 true? Select one or more: a. 9 b. 8 c. 5 d. 4 e. 6

f. 7 Question 92 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 93 Not yet answered Marked out of 1.00

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Question text If x divides 49, then x divides 30. Select one:

True False Question 94 Not yet answered Marked out of 1.00

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Question text Every straight line on the Cartesian plane intersects the x-axis. Select one: True False Question 95 Not yet answered Marked out of 1.00

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for y=sin(3x+4y)y=sin(3x+4y) Select one: a.

y1=3cos(3x+4y)1−4cos(3x+4y)y1=3cos(3x+4y)1−4cos(3x+4y)

b.

y1=3cos(3x+4y)1+4cos(3x+4y)y1=3cos(3x+4y)1+4cos(3x+4y)

c.

y1=3cos(3x−4y)1+4cos(3x−4y)y1=3cos(3x−4y)1+4cos(3x−4y)

d.

y1=3cos(3x−4y)1−4cos(3x−4y)y1=3cos(3x−4y)1−4cos(3x−4y) Clear my choice

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Question text Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only: 1. Write the equation of the line that represents the linear approximation to the function below at the given point a: f(x) = 12 - x2 ; a = 2 ; f(2.1) Answer: y = L(x) = Answer

x + Answer

2. Use linear approximation to estimate the given function value. f(2.1) = Answer 3. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact Percent error is: Answer

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%

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Question text

(Note: Answers should be in decimal form. Up to two decimal places only)

Largest possible slope: x = Answer y = Answer S = Answer Smallest possible slope: x = Answer y = Answer S = Answer Question 98 Not yet answered Marked out of 1.00

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Question text Find an equation of the line tangent to the graph of (x2+y2)3=8x2y2(x2+y2)3=8x2y2 at the point (-1,1) Select one: a. y - 1 = x + 2 b. y - 1 = x - 2 c. y + 1 = x - 2 d. y + 1 = x + 2 Clear my choice Question 99 Not yet answered Marked out of 5.00

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Question text A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. Given that variable x shall be the length of one edge of the square cu from each corner of the sheet of cardboard, what will be the dimensions of the box with largest volume? (Note: Answer should be in decimal form and up to two decimal places only)

x ≈ Answer

ft, so

Length = Answer Width = Answer

ft

Height = Answer V ≈ Answer

ft

ft

ft3

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Question text Given f(x) = 2x + 3. Evaluate (f°f)(x). Sample text answer: 3x^2+6x-7. Do not use space between the number, letter and symbol. Answer:Answer

CALCULUS 1 By: Grace Carticiano & Francheska Cuison

QUIZZES Quiz 3 The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=10 to t=30 seconds? (b) What was the average velocity of the car from t=20 to t=25 seconds? a) average velocity = Answer (b) average velocity = Answer

feet/second feet/second

The figure shows the temperature during a day in a place. How fast is the temperature changing from 1:00 P.M. to 7:00 P.M.? Round-off your answer to 2 decimal places. Answer: Answer

0

F/hour

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1) Answers: (a) A(2.5) = Answer (b) A(4) - A(1) = Answer

square units square units

For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o f(x). Note: For exponential answer, express it like x^3 for x cubed. Use lowercase letters, and do not put spaces in your answer. Answer: f o g(x) = Answer

3x^2+1

g o f(x) = Answer

9x^2-12x+5

Refer to the figure. Which of the following represents the graph drawn in red? Select one: a. | g(x) | b. g(x-1) c. [ g(x) ] d. g(x)-1

An enrollment slip indicates a specific down payment based from the number of units enrolled by a student as follows: for number of units from 1 to 9, down payment is Php 5000; for number of units from 10 to 15, down payment is Php 10,000; and a down payment of Php 15,000 for units from 16 to 21. Which of the multiline functions define E(d), the down payment due on specific number of units enrolled. Unit is of integer type.

Evaluate f(3), g(-1), and h(4). Answer: f(3) = Answer g(-1) = Answer h(4) = Answer

After evaluating g(-4), g(-1) and g(3), choose which graph represents the given conditions.

Answer:

A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function for T(x), the state income tax due on earnings of x dollars.

Answer:

Given g(x) = (x+3)/(x-1). Evaluate g(5) and g(2n+1). Note that fractional answers must be expressed like -5/6, and answers with exponents like (x^2-1)/(x+3). Use lower case letters.and do not use spaces in your answers. Answer: g(5) =Answer

and g(2n+1) =Answer

A function f is given by f(7-11x) = 3x3 - 10x. Evaluate f(-4). Answer: f(-4) =Answer

A FUNCTION assigns a unique output element in the range to each input element from the domain.

For y=f(x), x is the domain, and y is the range

Given f(x) = x3 - 4x2 +2, f(2) when evaluated is -6.

Which of the following figures represents the graph of a function? Select one: a. Figures 1 and 2 b. Figure 2 c. Figure 1 d. Figure 3 e. All of the figures f. Figures 1 and 3

Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)). Note: Do not use spaces in your answers. Answer: (Write your answer in this format: x+A+1) f(g(x)) =Answer g(f(x)) =Answer A =Answer

For f(x) = |9-x| and g(x) = sqrt(x-1). Evaluate fog(1). Answer: f(g(1) =Answer

Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any. Answers: (a) Answer

(b) Answer (c) Answer (d) Answer

Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = Answer

From the figure shown, find the values of f(2), f(-1) and f(0). Answers: f(2) =Answer f(-1) =Answer f(0) =Answer

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1). Answers: f(-3) = Answer f(-1) = Answer f(0) = Answer f(1) = Answer Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer -2f(1) = Answer What values of x will make the statement x+5=3 or x2=9. Answers: x = Answer

or

(x = Answer

and x = Answer

) <--- For this, write the least value first.

What is the slope of the line through (3,9) and (x,y) for y=x2 and x=2.97? x=3.001? x=3+h? What happens to this last slope when h is very small (close to 0)? Round-off your answers to 2 decimal places, whenever possible. Answers: (Write the letter first before the number, whenever possible.) Slope at x=2.97 = Answer Slope at x=3.001 = Answer Slope at x=3+h = Answer Slope when h is close to 0 = Answer What is the slope of the line through (2,4) and (x,y) for y = x2 + x - 2 and x=1.99? x=2.004? x=2+h. What happens to this last slope when h is very small? Answers: when x=1.99: m = Answer

Round-off your answer to 2 decimal places.

when x=2.004: m = Answer

Round-off your answers to 3 decimal places.

when x=2+h:m = Answer when h approaches 0: m = Answer What is the slope of the line through (-1,-2) and (x,y) for y = x2 + 2x + 1 and x=-0.90? x=-1.05? x=h-1? What happens to this last slope when h is very small? Round-off your answers to 2 decimal places whenever possible. Use the ^ symbol to express the exponent of a variable, i.e. x^2 (x squared). Do not use spaces on your answers Answers: when x=-0.90: m = Answer when x=-1.05: m = Answer when x=h-1: m = Answer

/h

when h approaches 0: m = Answer The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=0 to t= 20 sec? (b) What was the average velocity from t=10 to t=30 sec? (c) About how fast was the car traveling at t=15 sec?

Answers: (a) V = Answer

ft/sec

(b) V = Answer

ft/sec

(c) V = Answer

ft/sec

Define A(x) to be the area bounded by x and y axes, the line y=x+1, and the vertical line at x. (a) Evaluate A(2) and A(3) (b) What area would A(3) - A(1) represent? Answers: (a) A(2) = Answer

square units

(b) A(3) - A(1) = Answer

A(3) = Answer

square units

square units

The graph shows the population growth of bacteria on a petri plate. If at t=10 days, the population grows to 4600 bacteria, find the rate of population growth from t=9 to t= 10 days? Answer: rate of growth = Answer Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3. Answer: If x = - Answer

and x = Answer

then x2 + x - 6 is not equal to 0

QUIZ 4 The slope of the line through (5,15) and (x+8, x2-2x) isAnswer

Given g(t) = t+5t−1t+5t−1, evaluate: (a) g(5) and (b) g(2s - 5) Answer: (a) g(5) = Answer (b) g(2s-5) = Answer

.

Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer -2f(1) = Answer

Which of the following are negation of the statement: f(x) and g(x) are polynomials. Select one or more: a. f(x) or g(x) is a polynomial b. g(x) is a polynomial c. f(x) and g(x) are not polynomials d. f(x) is a polynomial Find the slope of the line through (-5,3) and (x+1, x-2). Answer: m = x-5/x+6

Write the contrapositive of the statement: If x>3, then x2>9. Use words or phrase for your answer. Answer: If x2 Answer

9, then x Answer

QUIZ 5 limx→0cos2x−1cosx−1limx→0cos2x−1cosx−1

Evaluate Answer: 4

3.

Write the contrapositive of the statement: I feel good when I jog. Answer: When I don't jog, I feel Answer: Bad

Evaluate

limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3

Answer: Answer

/ Answer

Write the negation of the statement: 8 is a prime number. Answer: 8 is Answer: not a prime number

Evaluate

limx→1x13−1x14−1limx→1x13−1x14−1

Answer: Answer

Evaluate

/ Answer

limx→103x−5−−−−−√5limx→103x−55

Answer: Answer

Every vertical line on the Cartesian plane intersects the x-axis. Select one: True False

Evaluate

limx→43−x+5−−−−√x−4limx→43−x+5x−4

Answer: - Answer Evaluate

/ Answer

limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5

Answer: Answer Which values of x will make the statement x+5=3 or x2=9 true?

Select one: a. (-2 and 3) or -3 b. -2 or (3 and -3) c. -2 and (3 or -3) d. (-2 or 3) and -3 Clear my choice

The sum of two prime numbers is a prime. True

QUIZ 6 Use the function h defined by the graph shown to determine the following limits:

limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3) (a)

Answers: (a) Answer (b) Answer

At which values of x is the function discontinuous?Answers:

f(x)=x2+x−6x−2f(x)=x2+x−6x−2continuous and

continuous at x = Answer discontinuous at x = Answer Use the function h defined by the graph below to determine the following limits:

limx→2x+h(x)limx→2x+h(x) (b) limx→3h(x2) (a)

Answers: (a) Answer

(b) Answer Use the graph below to determine the right-hand limit of the function f(x) at: (a) x=-2 (b) x=10 Answers: (a) Answer (b) Answer

Use the functions f and g defined by the graphs as shown to determine the following limits:

limx→1(f(x)xg(x))limx→1(f(x)xg(x)) (b) limx→1f(g(x)) (a)

Answers: (a) Answer (b) Answer Use the function h defined by the graph below to determine the following limits:

limx→2(xlimx→2(x . h(x−1))h(x−1)) (b) limx→0h(3+x)−h(3)h(x) (a)

Answers: (a) Answer (b) Answer At which values of x is the function from the graph shown continuous? State the answers from the least to the highest, if there would be more than one. Answer: x = Answer Use the function f defined by the graph shown to determine the following limits: (a)

limx→1+f(x)limx→1+f(x)

lim

(b) x→1− Answers:

f(x)

(a) Answer (b) Answer Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x2 - 2 on [0,3] Answer: Answer Use the function h defined by the graph as shown to determine the following limits:

limx→2h(2x−2)limx→2h(2x−2) (b) limx→2h(1+x) (a)

Answers: (a) Answer (b) Answer

MIDTERM EXAM If a and b are real numbers, then (a+b)2 = a2+b2. Select one: True False Which of the following is the contrapositive for the statement: If your car is properly tuned, it will get at least 24 miles per gallon. Select one: a. If your car will not get at least 24 miles per gallon, then it is not properly tuned. If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function.

Select one: True False Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1). Answers: (a) Answer

- Answer

2

(b) Answer

- Answer

2

(c) Answer

x2 + Answer

Which of the following will make the statement x2+3 > 1 true? Select one: a. x = -1 b. x is greater than or equal to -1 c. x > -1 d. x is less than or equal to -1

Let f(x) = 1-(x-1)2 evaluate Answers:

(a)f(2)f(3) and (b)f(23)(a)f(2)f(3) and (b)f(23)

(a) Answer (b) Answer

Find the slope of the line through (-3-1) and (x+3, y+1). Answer: Answer

From the graph shown, find: a. f(-1) b. f(0)

c. 3f(2) d. the value of x that corresponds to f(x)=0 Answers: a. f(-1) = Answer b. f(0) = Answer c. 3f(2) = Answer

-14

d. x = 0 Let A = {1,2,3,4,5}, B = {0,2,4,6}, and C = {-2,-1,0,1,2,3}. Which of the values of x will satisfy each statement? Select one: a. x is in A or x is in C b. x is in A and x is in B c. x is not in B and x is in C

Calculus 1 Prelim to Midterm! Quiz 1 Sketch the lines x=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew. (2 answers) -The slope of the tangent line at x=2 is 0. -The slope of the tangent lines at x=1 is 1 and at x=3 is -1

The slope of a vertical line is -undefined

The slope of the tangent line is called the -Derivative

The slope of a horizontal line is

0

The process of taking the limit of a sum of little quantities is called -Integration

The 2 divisions of Calculus are: -Integral -Differential

If a tangent line is inclined 45 degrees, then what is the slope the tangent line? 1

Calculus was developed by Leibniz and -Newton

The following problems could be solved by differential calculus: (2 answers) - largest or smallest volume of a solid - rate or speed

Quiz 2! Find the equation of the line passing through (-2,3) and perpendicular to the line 4x=9-2y. Use the general equation of the line for your final answer.

Find the slope of the line which is tangent to the circle with center C(3,1) at the point P(8,13).

Find the length and midpoint of the interval from x=9 to x=-2. (use decimal values for fractional answer)

Find the equation of the line which goes through the point (3,10) and is parallel to the line 7x-y=1.

Find the slope of the line passing through the points (3,-4) and (-6,9). Use decimal value for your final answer.

Find the slope and midpoint of the line segment from P(2,-3) to Q(2+n,-3+5n).

Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x=2. (write the numerical coefficient of each term to complete the required equation)

Find an equation describing all points P(x,y) equidistant from Q(-3,4) and R(1,-3). (use the general equation of a line - input the numerical coefficient of each term of the equation below)

Find the equation of a circle with radius=6 and center C(2,-5). (write the required exponent after the ^ symbol; write the numerical coefficient of each term to complete the required equation)

Quiz 3 Refer to the figure. Which of the following represents the graph drawn in red?

An enrollment slip indicates a specific down payment based from the number of units enrolled by a student as follows: for number of units from 1 to 9, down payment is Php 5000; for number of units from 10 to 15, down payment is Php 10,000; and a down payment of Php 15,000 for units from 16 to 21. Which of the multiline functions define E(d), the down payment due on specific number of units enrolled. Unit is of integer type.

Consider the equation below: After evaluating g(-4), g(-1) and g(3), choose which graph represents the given conditions.

The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=10 to t=30 seconds? (b) What was the average velocity of the car from t=20 to t=25 seconds?

For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o f(x).

Note: For exponential answer, express it like x^3 for x cubed. Use lowercase letters, and do not put spaces in your answer. Answer: f o g(x) = 3x^2+1 g o f(x) = 9x^2-12x+5

A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function for T(x), the state income tax due on earnings of x dollars.

The figure shows the temperature during a day in a place. How fast is the temperature changing from 1:00 P.M. to 7:00 P.M.? Round-off your answer to 2 decimal places.

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1)

Quiz 4 Let f(x)=-1-x-2x2, evaluate f(x+h)−f(x)h Factor out the negative sign for the final answer, if any.

Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1).

Let f(x) = 2-x2, evaluate (a) f(x+1) and (b) f(x)+f(1).

The slope of the line through (5,15) and (x+8, x2-2x) is

Which graph represents the function

Given g(t) = t+5t−1, evaluate: (a) g(5) and (b) g(2s - 5) a) 5/2 b) s/s-3 Which graph corresponds to f(x)=x−−√?

From the figure shown, find the values of f(2), f(-1) and f(0).

If a and b are real numbers, then (a+b)2 = a2+b2. -False

If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function. -False

Let f(x) = 1-(x-1)2 evaluate (a)f(2)f(3) and (b)f(23) a) 0 b) 8/9

Let A = {1,2,3,4,5}, B = {0,2,4,6}, and C = {-2,-1,0,1,2,3}. Which of the values of x will satisfy each statement? = x is in A or x is in C

From the graph shown, find: a. f(-1) b. f(0) c. 3f(2) d. the value of x that corresponds to f(x)=0

Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1).

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1).

Which of the following is the contrapositive for the statement: If your car is properly tuned, it will get at least 24 miles per gallon. -If your car will not get at least 24 miles per gallon, then it is not properly tuned

Find the slope of the line through (-5,3) and (x+1, x-2). x-5/x+6

Find the slope of the line through (-3-1) and (x+3, y+1). y+2/x+6 (wrong) y/x(wrong) x-5/x+6 (try)

Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any. a) 3x-10 b) 3x-6 c) -1/5 d) -3

Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = x+1

Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1).

Evaluate f(3), g(-1), and h(4). f(3) = 1 g(-1) = -2 h(4) = 1

Which of the following will make the statement x2+3 > 1 true? x is greater than or equal to -1

Use chain rule to calculate dydxdydx of

y=cos4(7x3)y=cos4(7x3) Select one: a. dydx=−84x2cos3(7x3)sin(7x3)dydx=−84x2cos3(7x3)sin(7x3)

b. dydx=−84x2cos3(7x3)+sin(7x3)dydx=−84x2cos3(7x3)+sin(7x3)

c. dydx=84x2cos3(7x3)+sin(7x3)dydx=84x2cos3(7x3)+sin(7x3)

d. dydx=84x2cos3(7x3)sin(7x3)dydx=84x2cos3(7x3)sin(7x3)

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Assume that y is a function of x. Find y1=dydxy1=dydx for (x−y)2=x+y−1(x−y)2=x+y−1 Select one: a. y1=2y−2x+12y−2x−1y1=2y−2x+12y−2x−1

b. y1=2y+2x−12y−2x+1y1=2y+2x−12y−2x+1

c. y1=2y−2x+12y+2x−1y1=2y−2x+12y+2x−1 d. y1=2y+2x−12y+2x+1y1=2y+2x−12y+2x+1

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If a and b are real numbers then (a + b)2 = a2 + b2. Select one: True False Question 4 Answer saved Marked out of 2.00

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Find a value for B so that the line y = 10x – B, goes through the point (5,-5). Answer: B = Answer

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(Note: Answers should be in decimal form. Up to two decimal places only)

Largest possible slope: x = Answer y = Answer S = Answer

Smallest possible slope: x = Answer y = Answer S = Answer Question 6 Answer saved Marked out of 1.00

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Evaluate

limx→4x−−√−2x−4limx→4x−2x−4

Answer: Answer

/ Answer

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Use chain rule to calculate dydxdydx of

y=(5x2+11x)20y=(5x2+11x)20 Select one:

a. dydx=(−20)(5x2+11x)19(10x+11)dydx=(−20)(5x2+11x)19(10x+11)

b. dydx=(−20)(5x2+11x)19(10x−11)dydx=(−20)(5x2+11x)19(10x−11)

c. dydx=(20)(5x2+11x)19(10x−11)dydx=(20)(5x2+11x)19(10x−11) d. dydx=(20)(5x2+11x)19(10x+11)dydx=(20)(5x2+11x)19(10x+11)

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The slope of the line from point U(5,13) and the point V(x+1, x 2-3) is Answer . Question 9 Answer saved Marked out of 1.00

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Write the contrapositive of the statement: If x>3, then x2>9. Use words or phrase for your answer. Answer: If x2 Answer

9, then x Answer

3.

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Use linear approximations to estimate 1–√46146. Choose a value of "a" to produce a small error. Note: Answers should be in decimal form. Up to two decimal places only.

1–√46=f(146)≈L(146)146=f(146)≈L(146) = Answer Question 11 Answer saved Marked out of 1.00

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Assume that y is a function of x. Find y1=dydxy1=dydx for y=sin(3x+4y)y=sin(3x+4y) Select one:

a. y1=3cos(3x−4y)1−4cos(3x−4y)y1=3cos(3x−4y)1−4cos(3x−4y)

b. y1=3cos(3x+4y)1+4cos(3x+4y)y1=3cos(3x+4y)1+4cos(3x+4y)

c. y1=3cos(3x+4y)1−4cos(3x+4y)y1=3cos(3x+4y)1−4cos(3x+4y)

d. y1=3cos(3x−4y)1+4cos(3x−4y)y1=3cos(3x−4y)1+4cos(3x−4y)

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Fill in the missing the numbers to find the correct answer/s: Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.

P = xy2

Answers:

x = Answer

y = Answer P = Answer Question 13 Answer saved Marked out of 1.00

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Use Newton's Method to find the root of x4−5x3+9x+3=0x4−5x3+9x+3=0 accurate to six decimal places in the interval [4,6]. (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer

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Which of the following equations is the line perpendicular to 2x – 3y = 9? Select one:

a. 3x + 2y =11 b. 3x + 2y =10 c. 2x – 3y =11 d. 3x – 2y = 10 Clear my choice Question 15 Answer saved Marked out of 1.00

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Find an equation of the line tangent to the graph of (x2+y2)3=8x2y2(x2+y2)3=8x2y2 at the point (-1,1) Select one: a. y + 1 = x - 2 b. y - 1 = x + 2 c. y - 1 = x - 2 d. y + 1 = x + 2 Clear my choice Question 16 Answer saved Marked out of 1.00

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What is the slope of the tangent line through (3,2) and (x,y) for x=-2 and y=x3. Answer: m = Answer Question 17 Answer saved Marked out of 2.00

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Given f(x) = 2x + 3. Evaluate . Sample text answer: 3x^2+6x-7. Do not use space between the number, letter and symbol. Answer: Answer Question 18 Answer saved Marked out of 1.00

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Which of the following are integer values of x that will make the statement x3 + 3 > 1 true? Select one: a. x = 1 b. x < -1 c. x is less than or equal to -1

d. x is greater than or equal to -1 Clear my choice Question 19 Not yet answered Marked out of 1.00

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Answers: (a) Answer (b) - Answer (c) Answer Question 20

/ Answer / Answer

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Write the contrapositive of the statement: If I exercise and eat right, then I will be healthy. Don't use contractions in your answer. Answer: If I Answer eat right.

healthy, then I Answer

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Determine whether the graph is continuous or not continuous.

Select one: a. Continuous

exercise and

b. Not Continuous Clear my choice Question 22 Answer saved Marked out of 2.00

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Let f(x) = (x-1)2 and define S(x) to be the slope of the line through the point (0,0) and (x,f(x)). Evaluate S(6). Answer: S(6) = Answer (Use fractional answer when possible, say 12/13. Do not use space between symbol and number.) Question 23 Answer saved Marked out of 2.00

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(Note: Answer should be in decimal form. Up to two decimal places only)

x ≈ Answer

θ = Answer

ft.

degrees.

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Consider the function below.

limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5? Select one: a. If x is within 1 unit distance of 1, then f(x) is within 0.05 unit of 5. b. If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5.

c. If x is within 0.98 unit distance of 1, then f(x) is within 0.05 unit of 5. d. If x is within 1.02 units distance of 1, then f(x) is within 0.05 unit of 5. Clear my choice Question 25 Answer saved Marked out of 2.00

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(Note: Answers should be in decimal form. Up to two decimal places only) x = Answer Smallest sum: S = Answer Question 26

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For the function f(x)=x(x2+1)2f(x)=x(x2+1)2 on [-2,2]

Find the critical points and the absolute extreme values of f on the given interval. Select one: a. x=±12−−√x=±12 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:: 33√163316

b. x=±23−−√x=±23 as the critical points absolute maximum value of f: −33√16−3316 absolute minimum value of f: 33√163316

c. x=±13−−√x=±13 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:33√163316 d. x=13−−√x=13 as the critical points absolute maximum value of f: −33√16−3316 absolute minimum value of f: −33√16−3316

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Use implicit differentiation to find dydxdydx,

x3=x+yx−yx3=x+yx−y Select one: a. y1=3x2(x−y)2+2y2xy1=3x2(x−y)2+2y2x

b. y1=3x2(x+y)2−2y2xy1=3x2(x+y)2−2y2x

c. y1=3x2(x−y)2−2y2xy1=3x2(x−y)2−2y2x

d. y1=3x2(x+y)2+2y2xy1=3x2(x+y)2+2y2x

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Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen? (Note: Answers should be in decimal form. Up to two decimal places only)

x = Answer

ft.

y = Answer

ft.

A = Answer

ft2

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Use chain rule to calculate dydxdydx of

y=e−x2y=e−x2 Select one: a. dydx=−2x−x2dydx=−2x−x2

b. dydx=2x−x2dydx=2x−x2 c. dydx=−2xx2dydx=−2xx2

d. dydx=2xx2dydx=2xx2

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If f(x) and g(x) are linear functions then f(x)g(x) is a linear function. Select one: True False Question 31 Answer saved Marked out of 1.00

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Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x2 - 2 on [0,3] Answer: Answer Question 32 Answer saved Marked out of 1.00

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Assume that y is a function of x. Find y1=dydxy1=dydx for x−y3y+x2=x+2x−y3y+x2=x+2 Select one: a. y1=1−y+3x2−4x3y2+x+2y1=1−y+3x2−4x3y2+x+2 b. y1=1−y−3x2−4x3y2−x+2y1=1−y−3x2−4x3y2−x+2 c. y1=1−y−3x2−4x3y2+x+2y1=1−y−3x2−4x3y2+x+2 d. y1=1−y+3x2−4x3y2+x−2 Determine all the critical points for the function.

f(x)=xex2f(x)=xex2 Select one: a. 1, ∞∞ b. does not have any critical points c. 1, 2 d. 0 Clear my choice Question 34 Answer saved Marked out of 1.00

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The equation of motion is given by s(t) = 6t2 + t + 8 at 1:05 P.M. What is the average velocity from 1:07 P.M. to 1:09 P.M. in meters/second? Answers: @ 1:07 P.M., t = Answer

minutes; s(t) = Answer

meters

@ 1:09 P.M., t = Answer

minutes; s(t) = Answer

meters

Average velocity = Answer Question 35 Answer saved Marked out of 1.00

m/sec

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Every vertical line on the Cartesian plane intersects the x-axis. Select one: True False Question 36 Answer saved Marked out of 1.00

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Consider the function below.

limx→3x2=9limx→3x2=9 What values of x guarantee that 0.62 units of 9?

If x is within Answer units of 9. Question 37

f(x)=x2f(x)=x2 is within

units of 3, then f(x) is within 0.62

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Find a linear approximation of f(x)=3xe2x−10f(x)=3xe2x−10 at x = 5. (Note: Fill in the missing numbers to get the get the correct answer. Answers should be in decimal form. Up to two decimal places only.) L(x) = Answer

+ Answer

(x - 5) = Answer

x + Answer

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Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 39 Answer saved Marked out of 1.00

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Find the local extreme values of the given function: f(x)=x4−6x2f(x)=x4−6x2

Select one: a. Local minimum: (1.73, -9) Local maximum: (-1.73, -9) b. Local minimum: (1.73, 9) Local maximum: (-1.73, 9) c. Local minimum: (-1.73, -9) Local maximum:(1.73, -9) d. Local minimum: (-1.73, 9) Local maximum: (1.73, 9) Clear my choice Question 40 Answer saved Marked out of 3.00

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Consider a rectangle of perimeter 12 inches. Form a cylinder by revolving this rectangle about one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume? (Note: Answer should be in decimal form. Up to two decimal places only)

r = Answer

ft

h = Answer

ft

V ≈ Answer Question 41 Answer saved

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An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions will result in a box with the largest possible volume?

Answers:

x = Answer

ft.

y = Answer

ft.

V = Answer

ft.3

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If x divides 49, then x divides 30. Select one: True False Question 43 Answer saved Marked out of 1.00

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You will cut two boards (exactly the same length after the cut) and place them end to end. Suppose the combined length must be within 0.06 inch of 30 inches. Then each board must be within how many inches of 15? Select one: a. If each board is within 0.03 inch distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches. b. If each board is within 14.97 inches distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches. c. If each board is within 15.03 inches distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches. d. If each board is within 15 inches distance of 15 inches, then the combined length of the boards is within 0.06 inch of 30 inches. Clear my choice

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Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only:

1. Write the equation of the line that represents the linear approximation to the function below at the given point a: f(x) = 12 - x2 ; a = 2 ; f(2.1) Answer: y = L(x) = Answer

x + Answer

2. Use linear approximation to estimate the given function value. f(2.1) = Answer 3. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact Percent error is: Answer

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%

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Find the point of intersection and the angle between 2x - 3y = 3 and 4x - 2y = 10. Answers: Point of Intersection = ( Answer

, Answer

Angle of Intersection = Answer

0

)

(round-off to 2 decimal places)

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Consider the function below.

limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.9 unit of 5? Select one: a. If x is within 0.7 unit distance of 1, then f(x) is within 0.9 unit of 5. b. If x is within 1 unit distance of 1, then f(x) is within 0.9 unit of 5. c. If x is within 1.3 units distance of 1, then f(x) is within 0.9 unit of 5. d. If x is within 0.3 unit distance of 1, then f(x) is within 0.9 unit of 5. Clear my choice

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Evaluate limx→23x2−x−10x2−4limx→23x2−x−10x2−4 Answer: Answer

/ Answer

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Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.

(Note: Answers should be in decimal form. Up to two decimal places only)

r ≈ Answer h ≈ Answer

V ≈ Answer

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Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 50 Answer saved Marked out of 4.00

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Find a linear approximation to h(t)=t4−6t3+3t−7h(t)=t4−6t3+3t−7 at t=−3t=−3. (Note: Complete the linear approximation by filling in the missing numbers. Answers should be in decimal form. Up to two decimal places only)

L(t) = Answer Question 51 Answer saved

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(t + 3) = Answer

t - Answer

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Use linear equation to estimate e0.06. Choose a value of 'a' to produce a small error. Note: Answers should be in decimal form. Up to two decimal places only. e0.06 = Answer Question 52 Answer saved Marked out of 1.00

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Determine all the critical points for the function.

f(x)=x2ln(3x)+6f(x)=x2ln(3x)+6 Select one: a. 0 b. no correct answer c. 0.20 d. 0.50 Clear my choice Question 53 Answer saved

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You are standing at the edge of a slow-moving river which is one mile wide and wish to return to your campground on the opposite side of the river. You can swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the campground, which is one mile from the point directly across the river from where you start your swim. What route will take the least amount of time? (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer

mi.

Shortest possible time: T ≈ Answer Question 54

hr.

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A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. Given that variable x shall be the length of one edge of the square cu from each corner of the sheet of cardboard, what will be the dimensions of the box with largest volume? (Note: Answer should be in decimal form and up to two decimal places only)

x ≈ Answer

ft, so

Length = Answer Width = Answer

ft ft

Height = Answer

V ≈ Answer

ft

ft3

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Use implicit differentiation to find dydxdydx (xy+1)3=x−y2+8(xy+1)3=x−y2+8

Select one: a. y1=1−3y(xy+1)23x(xy+1)2+2yy1=1−3y(xy+1)23x(xy+1)2+2y

b. y1=1+3y(xy+1)23x(xy+1)2−2yy1=1+3y(xy+1)23x(xy+1)2−2y

c. y1=1+3y(xy+1)23x(xy+1)2+2yy1=1+3y(xy+1)23x(xy+1)2+2y

d. y1=2y+2x−12y−2x+1y1=2y+2x−12y−2x+1

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Consider the function below. (\Large \lim_{x \rightarrow 3} (2x + 1) = 7 \)

What values of x guarantee that f(x) = 2x + 1 is within 0.04 units of 7?

If x is within Answer units of 7.

units of 3, then f(x) is within 0.04

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Evaluate limx→π4sinx+cosxtanxlimx→π4sinx+cosxtanx Answer: Answer Question 58 Answer saved Marked out of 1.00

Round-off your answer to 2 decimal places.

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Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 59 Answer saved Marked out of 1.00

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Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 60 Answer saved Marked out of 1.00

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Assume that y is a function of x. Find y1=dydxy1=dydx for y=x2y3+x3y2y=x2y3+x3y2 Select one: a. y1=2xy3+3x2y21+3x2y2−2x3yy1=2xy3+3x2y21+3x2y2−2x3y

b. y1=2xy3+3x2y21−3x2y2+2x3yy1=2xy3+3x2y21−3x2y2+2x3y

c. y1=2xy3+3x2y21−3x2y2−2x3yy1=2xy3+3x2y21−3x2y2−2x3y

d. y1=2xy3+3x2y21+3x2y2+2x3yy1=2xy3+3x2y21+3x2y2+2x3y

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Use chain rule to calculate dydxdydx of

y=sin(4x3+3x+1)y=sin(4x3+3x+1) Select one: a. dydx=(12x2−3)cos)4x3+3x+1)dydx=(12x2−3)cos)4x3+3x+1)

b. dydx=(12x2+3)cos(4x3+3x+1)dydx=(12x2+3)cos(4x3+3x+1)

c. dydx=(12x2+3)cos(4x3+3x−1)dydx=(12x2+3)cos(4x3+3x−1)

d. dydx=(12x2−3)cos(4x3+3x−1)dydx=(12x2−3)cos(4x3+3x−1)

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Which of the following is the appropriate multiline function for the graph shown?

Select one:

a.

b.

c. Clear my choice Question 63 Answer saved Marked out of 1.00

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Identify the absolute extrema and relative extrama for the following function.

f(x)=x3f(x)=x3 on [-2,2]

Select one: a. The function has an absolute maximum of -8 at x = 2 and absolute minimum of 8 at x = -2. The function has no relative extrema. b. The function has an absolute maximum of 8 at x = 2 and absolute minimum of 8 at x = -2. The function has no relative extrema. c. The function has an absolute maximum of 8 at x = -2 and absolute minimum of -8 at x = 2. The function has a relative minimum of (0,0) and no relative maxmum. d. The function has an absolute maximum of 8 at x = 0 and absolute minimum of 8 at x = -1. The function has a no relative extrema. Clear my choice Question 64 Answer saved Marked out of 1.00

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Locate the critical points of the following functions. Then use the second derivative test to determine whether they correspond to local minima or local maxima or whether the test is inconclusive.

p(x)=x−4x2+20p(x)=x−4x2+20 Select one: a. Critical points: (2, -1/4) and (10, -1/2) Local minimum: x = 2 Local maximum: x = 10 b. Critical points: (1, -1/4) and (2, -1/20) Local minimum: x = -2 Local maximum: x = 5 c. Critical points: (2, -1/4) and (10, -1/20) Local minimum: x = -2 Local maximum: x = 10 d. Critical points: (2, -3/4) and (10, -1/20) Local minimum: x = -20 Local maximum: x = 1 Clear my choice Question 65 Answer saved Marked out of 1.00

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Which of the following is the contrapositive of the statement: If you love your country, you will vote for me. Select one: a. If you love your country, then you will vote for me. b. If you don't love your country, then you will vote for me. c. If you don't vote for me, then you don't love your country. d. If you don't love your country, then you won't vote for me. Clear my choice

Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 67 Answer saved Marked out of 1.00

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Use implicit differentiation to finddydxdydx

exy=2yexy=2y

Select one: a. y1=yexy2−xexyy1=yexy2−xexy

b. y1=yexy2+xexyy1=yexy2+xexy

c. y1=yexy2−exxyy1=yexy2−exxy

d. y1=yexy2+exxyy1=yexy2+exxy

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Evaluate limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3 Answer: Answer Question 69

/ Answer

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Do the following. Type your answer on the space/s provided. Up to two decimal places only.

1. Write the equation of the line that represents the linear approximation to the function below at the given point a.

f(x)=e2;a=0;f(0.05)f(x)=e2;a=0;f(0.05) f(a) = Answer

2. Use the linear approximation to estimate the given function value. f(0.05) ≈ L (0.05) = Answer 3. Compute the percent error in your approximation. Percent error ≈ Answer Question 70 Answer saved Marked out of 1.00

%

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Use Newton's Method to find the root of 2x2+5=ex2x2+5=ex accurate to six decimal places in the interval [3,4]. (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer Question 71 Answer saved Marked out of 1.00

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For all positive real numbers a and b, if a > b, then a2 > b2. Select one: True False Question 72 Answer saved

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There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?

x = Answer

additional trees

P = Answer

apples

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A container in the shape of a right circular cylinder with no top has surface area 3 ft.2 What height h and base radius r will maximize the volume of the cylinder?

(Note: answers should be in decimal form. Up to two decimal places only)

r = Answer

ft.

h = Answer

ft.

ft3

V = Answer Question 74 Answer saved

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(Note: Answers should be in decimal form only. Up to two decimal places}

x ≈ Answer

ft.

y ≈ Answer

ft.

L ≈ Answer

ft.

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Use chain rule to calculate dydxdydx of y = tan (e3x√)(e3x)

Select one: a. dydx=−sec2(e3x−−√)3e3x√23x−−√dydx=−sec2(e3x)3e3x23x

b. dydx=−sec2(e3x−−√)2e3x√33x−−√dydx=−sec2(e3x)2e3x33x

c. dydx=sec2(e3x−−√)3e3x√23x√dydx=sec2(e3x)3e3x23x

d. dydx=sec2(e3x−−√)2e3x√33x−−√dydx=sec2(e3x)2e3x33x

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Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 77 Answer saved Marked out of 1.00

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Use the function h defined by the graph below to determine the following limits: (a) limx→2x+h(x)limx→2x+h(x) (b) limx→3h(x2)limx→3h(x2)

Answers: (a) Answer (b) Answer Question 78 Answer saved Marked out of 1.00

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Assume that y is a function of x. Find y1=dydxy1=dydx for cos2x+cos2y=cos(2x+2y)cos2x+cos2y=cos(2x+2y) Select one: a. y1=cosxsinx+sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx+sin(2x+2y)sin(2x+2y)−cosysiny

b. y1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysiny

c. y1=cosxsinx−sin(2x+2y)sin(2x+2y)+cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)+cosysiny

d. y1=cosxsinx+sin(2x+2y)sin(2x+2y)+cosysinyy1=cosxsinx+sin(2x+2y)sin(2x+2y)+cosysiny

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Consider the function below.

limx→2x3=8limx→2x3=8 What values of x guarantee that f(x) = x^3 is within 0.05 unit of 8? Select one: a. If x is within 2 units distance of 2, then f(x) is within 0.05 unit of 8. b. If x is within 1.99 units distance of 2, then f(x) is within 0.05 unit of 8.

c. If x is within 0.01 unit distance of 2, then f(x) is within 0.05 unit of 8. d. If x is within 2.01 units distance of 2, then f(x) is within 0.05 unit of 8. Clear my choice Question 80 Answer saved Marked out of 2.00

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Given f(x) = 2x + 3 and g(x) = x2. Evaluate . Sample text answer: 3x^2+6x-7. Do not use space between the number, letter and symbol. Answer: Answer Question 81 Answer saved Marked out of 1.00

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Evaluate

limh→05h+4−−−−−√−2hlimh→05h+4−2h

Answer: Answer

/ Answer

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Find an equation of the line tangent to the graph of x2+(y−x)3=9x2+(y−x)3=9 at x=1 Select one: a. y=76x+136y=76x+136

b. y=136x+76y=136x+76

c. y=136x−76y=136x−76

d. y=76x−136y=76x−136 Clear my choice Question 83 Answer saved Marked out of 1.00

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Find the slope and concavity of the graph pf x2y+y4=4+2xx2y+y4=4+2x at the point (1,1) Select one: a. Slope = 5454, Concavity = downward

b. Slope = 4545, Concavity = downward

c. Slope = 2525, Concavity = downward

d. Slope = 4545, Concavity = upward Clear my choice Question 84 Answer saved Marked out of 3.00

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Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only:

1. Write the equation of the line that represents the linear approximation to the function below at a given point a. f(x) = ln(1 + x); a = 0; f(0.9) y = L(x) = Answer 2. Use linear approximation to estimate the given function value. f(0.9) = Answer 3. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact Percent error: Answer

%

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A hotel charges Php1,500 per night for a room during the tourist season from June 1 through September 15, and Php1,200 per night otherwise. Define a multiline function which describes these rates. f(x) is the cost for one night on date x . Choose from the options. Select one:

a.

b.

c. Clear my choice Question 86 Answer saved Marked out of 1.00

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Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 87 Answer saved Marked out of 3.00

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Find the point of intersection and the angle between y = 4 - 2x and x - y = -1. Answers: Point of Intersection = ( Answer Angle of Intersection = Answer

, Answer 0

)

(round-off to 2 decimal places)

Question 88 Answer saved Marked out of 1.00

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Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 89 Answer saved Marked out of 1.00

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Find an equation of the line tangent to the graph of y=x2+sinπ2xy=x2+sinπ2x at x = -1 Select one: a. y = 2x + 2 b. y = -2x + 2 c. y = -2x - 2 d. y = 2x - 2 Clear my choice Question 90 Answer saved Marked out of 2.00

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Which of the following equations is the line perpendicular to 4y – 7x = 5? Select one: a. 4x + 7y + 18 = 0 b. 4y – 7x + 9 = 0

c. 7x – 4y + 9 = 0 d. 4x + 7y – 18 = 0 Clear my choice Question 91 Answer saved Marked out of 1.00

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Use chain rule to calculate dydxdydx of

y=x2sec(5x)y=x2sec(5x) Select one: a. dydx=2xsec(5x)+5x2sec(5x)tan(5x)dydx=2xsec(5x)+5x2sec(5x)tan(5x)

b. dydx=−2xsec(5x)+5x2sec(5x)tan(5x)dydx=−2xsec(5x)+5x2sec(5x)tan(5x)

c. dydx=2xsec(−5x)+5x2sec(5x)tan(5x)dydx=2xsec(−5x)+5x2sec(5x)tan(5x)

d. dydx=2xsec(5x)−5x2sec(5x)tan(5x)dydx=2xsec(5x)−5x2sec(5x)tan(5x)

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Use the graph below to determine the right-hand limit of the function f(x) at: (a) x=-2 (b) x=10

Answers: (a) Answer

(b) Answer Question 93 Answer saved Marked out of 1.00

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Determine all the critical points for the function

y=6x−4cos(3x)y=6x−4cos(3x) x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,... x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,...

Select one: a. 1.2217; 0.9199 b. 1.2217; 1.9199 c. 1.1991; 1.7122 d. 1.7991; 1.2217 Clear my choice Question 94 Answer saved Marked out of 1.00

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Use Newton's Method to determine x2x2 for f(x)=xcos(x)−x2f(x)=xcos(x)−x2 if x0=1x0=1 (Note: Answers should be in decimal form. Up to two decimal places only.)

x2 = Answer Question 95 Answer saved Marked out of 3.00

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Given a multiline function

Which of the following represents its graph for y=g(x) and Select one:

a.

b.

c.

d. Clear my choice

Question 96 Answer saved Marked out of 3.00

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Find the point of intersection and the angle between x - y = 32 and 3x - 8y = 6. Answers: Point of Intersection = ( Answer

, Answer

Angle of Intersection = Answer

0

)

(round-off to 2 decimal places)

Question 97 Answer saved Marked out of 1.00

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Use the function h defined by the graph shown to determine the following limits: (a) limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3)limx→0h(3+x)−h(3)

Answers: (a) Answer (b) Answer Question 98 Answer saved Marked out of 2.00

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Consider the function below.

limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5? Select one: a. If x is within 0.98 unit distance of 1, then f(x) is within 0.05 unit of 5. b. If x is within 1.02 units distance of 1, then f(x) is within 0.05 unit of 5.

c. If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5. d. If x is within 1 unit distance of 1, then f(x) is within 0.05 unit of 5. Clear my choice Question 99 Answer saved Marked out of 1.00

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If f(x) and g(x) are linear functions, then f(x) + g(x) is a linear function. Select one: True False Question 100 Answer saved Marked out of 2.00

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(Note: Answers should be in decimal form only. Up to two decimal places only)

x = Answer y = Answer

CALCULUS 1 – MATH6100 By: Grace, Francheska, Cute, Kuya Lodi, Boss Franz

QUIZ 1 – Prelim Exam: The slope of a horizontal line is 0

Sketch the line x=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew. The slope of the tangent line x=2 is 0. The slope of the tangent lines at x=1, is 1 and at x=3 is -1. If a tangent line is inclined 45 degrees, then what is the slope the tangent line? 1 The slope of the tangent line is called the Derivatives The following problems could be solved by differential calculus: Largest or smallest volume of a solid Rate or speed The 2 divisions of Calculus are: Integral Differential The process of taking the limit of a sum of little quantities is called Integration Calculus was developed by Leibniz and Newton The slope of a vertical line is Undefined Find the equation of the line passing through (-2,3) and perpendicular to the line 4x=9-2y. Use the general equation of the line for your final answer. Answer: x – 2

y+8

=0

Find the equation of the line which goes through the point (3,10) and is parallel to the line 7x-y=1. Answer: 7

x – y – 11

=0

Find the length and midpoint of the interval from x=9 to x=-2. (use decimal values for fractional answer) Answer: length = 11

and midpoint x = 3.5

Find the slope of the line passing through the points (3,-4) and (-6,9). Use decimal value for your final answer. Answer: -1.44

Find the slope of the line which is tangent to the circle with center C(3,1) at the point P(8,13). Answer: slope of the tangent line = -5/12 Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x=2. (write the numerical coefficient of each term to complete the required equation) Answer: 3 x + 7 y + 29 = 0 Find an equation describing all points P(x,y) equidistant from Q(-3,4) and R(1,-3). (use the general equation of a line Answer: 8 x – 14 y + 15 = 0 Find the slope and midpoint of the line segment from P(2,-3) to Q(2+n,-3+5n). Answer: slope = 5 , midpoint(0.5n + 2 , 2.5 n-3) Find the equation of a circle with radius=6 and center C(2,-5). (write the required exponent after the ^ symbol; write the numerical coefficient of each term to complete the required equation) Answer: x^2 + y^2 - 4 x + 10 y – 7 = 0

QUIZ 3 – Midterm Exam: The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=10 to t=30 seconds? (b) What was the average velocity of the car from t=20 to t=25 seconds? a) average velocity = Answer (b) average velocity = Answer

feet/second feet/second

The figure shows the temperature during a day in a place. How fast is the temperature changing from 1:00 P.M. to 7:00 P.M.? Round-off your answer to 2 decimal places. Answer: Answer

0

F/hour

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1) Answers: (a) A(2.5) = Answer (b) A(4) - A(1) = Answer

square units square units

For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o f(x). Note: For exponential answer, express it like x^3 for x cubed. Use lowercase letters, and do not put spaces in your answer. Answer: f o g(x) = Answer g o f(x) = Answer

3x^2+1 9x^2-12x+5

Refer to the figure. Which of the following represents the graph drawn in red? Select one: a. | g(x) | b. g(x-1) c. [ g(x) ] d. g(x)-1

An enrollment slip indicates a specific down payment based from the number of units enrolled by a student as follows: for number of units from 1 to 9, down payment is Php

5000; for number of units from 10 to 15, down payment is Php 10,000; and a down payment of Php 15,000 for units from 16 to 21. Which of the multiline functions define E(d), the down payment due on specific number of units enrolled. Unit is of integer type.

Evaluate f(3), g(-1), and h(4). Answer: f(3) = Answer g(-1) = Answer h(4) = Answer After evaluating g(-4), g(-1) and g(3), choose which graph represents the given conditions.

Answer:

A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function for T(x), the state income tax due on earnings of x dollars.

Answer:

Given g(x) = (x+3)/(x-1). Evaluate g(5) and g(2n+1). Note that fractional answers must be expressed like -5/6, and answers with exponents like (x^2-1)/(x+3). Use lower case letters.and do not use spaces in your answers. Answer: g(5) =Answer

and g(2n+1) =Answer

A function f is given by f(7-11x) = 3x3 - 10x. Evaluate f(-4). Answer: f(-4) =Answer A FUNCTION assigns a unique output element in the range to each input element from the domain.

For y=f(x), x is the domain, and y is the range

Given f(x) = x3 - 4x2 +2, f(2) when evaluated is -6.

Which of the following figures represents the graph of a function?

Select one: a. Figures 1 and 2 b. Figure 2 c. Figure 1 d. Figure 3 e. All of the figures f. Figures 1 and 3

Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)). Note: Do not use spaces in your answers. Answer: (Write your answer in this format: x+A+1) f(g(x)) =Answer g(f(x)) =Answer A =Answer

For f(x) = |9-x| and g(x) = sqrt(x-1). Evaluate fog(1). Answer: f(g(1) =Answer

Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any. Answers: (a) Answer (b) Answer (c) Answer (d) Answer

Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = Answer

From the figure shown, find the values of f(2), f(-1) and f(0). Answers: f(2) =Answer f(-1) =Answer f(0) =Answer

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1). Answers: f(-3) = Answer f(-1) = Answer f(0) = Answer f(1) = Answer Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer -2f(1) = Answer What values of x will make the statement x+5=3 or x2=9. Answers: x = Answer

or

(x = Answer

and x = Answer

) <--- For this, write the least value first.

What is the slope of the line through (3,9) and (x,y) for y=x2 and x=2.97? x=3.001? x=3+h? What happens to this last slope when h is very small (close to 0)? Round-off your answers to 2 decimal places, whenever possible. Answers: (Write the letter first before the number, whenever possible.) Slope at x=2.97 = Answer Slope at x=3.001 = Answer Slope at x=3+h = Answer Slope when h is close to 0 = Answer What is the slope of the line through (2,4) and (x,y) for y = x2 + x - 2 and x=1.99? x=2.004? x=2+h. What happens to this last slope when h is very small? Answers: when x=1.99: m = Answer

Round-off your answer to 2 decimal places.

when x=2.004: m = Answer

Round-off your answers to 3 decimal places.

when x=2+h:m = Answer when h approaches 0: m = Answer What is the slope of the line through (-1,-2) and (x,y) for y = x2 + 2x + 1 and x=-0.90? x=-1.05? x=h1? What happens to this last slope when h is very small? Round-off your answers to 2 decimal places whenever possible. Use the ^ symbol to express the exponent of a variable, i.e. x^2 (x squared). Do not use spaces on your answers Answers: when x=-0.90: m = Answer when x=-1.05: m = Answer when x=h-1: m = Answer

/h

when h approaches 0: m = Answer The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=0 to t= 20 sec? (b) What was the average velocity from t=10 to t=30 sec? (c) About how fast was the car traveling at t=15 sec?

Answers: (a) V = Answer

ft/sec

(b) V = Answer

ft/sec

(c) V = Answer

ft/sec

Define A(x) to be the area bounded by x and y axes, the line y=x+1, and the vertical line at x. (a) Evaluate A(2) and A(3) (b) What area would A(3) - A(1) represent? Answers: (a) A(2) = Answer

square units

(b) A(3) - A(1) = Answer

A(3) = Answer

square units

square units

The graph shows the population growth of bacteria on a petri plate. If at t=10 days, the population grows to 4600 bacteria, find the rate of population growth from t=9 to t= 10 days? Answer: rate of growth = Answer Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3. Answer: If x = - Answer

and x = Answer

then x2 + x - 6 is not equal to 0

The slope of the line through (5,15) and (x+8, x2-2x) isAnswer

Given g(t) = t+5t−1t+5t−1, evaluate: (a) g(5) and (b) g(2s - 5) Answer: (a) g(5) = Answer (b) g(2s-5) = Answer

5/2 s/s-3

.

Let f(x) = -x4-x-1, evaluate f(-1) and -2f(1). Answers: f(-1) = Answer

-1

-2f(1) = Answer

6

Let f(x)=-1-x-2x2, evaluate f(x+h)−f(x)hf(x+h)−f(x)h Factor out the negative sign for the final answer, if any. Answer: -(4x+2h+1)

Which of the following are negation of the statement: f(x) and g(x) are polynomials. Select one or more: a. f(x) or g(x) is a polynomial b. g(x) is a polynomial c. f(x) and g(x) are not polynomials d. f(x) is a polynomial Find the slope of the line through (-5,3) and (x+1, x-2). Answer: m = Answer x-5/x+6

Write the contrapositive of the statement: If x>3, then x2>9. Use words or phrase for your answer. Answer: If x2 Answer

9, then x Answer

Let f(x) = 2-x2, evaluate (a) f(x+1) and (b) f(x)+f(1). Answers: (a) f(x=1) = -x2- 2x+1 (b) f(x) + f(1) = -x2+3

3.

If a and b are real numbers, then (a+b)2 = a2+b2. Select one: True False Which of the following is the contrapositive for the statement: If your car is properly tuned, it will get at least 24 miles per gallon. Select one: a. If your car will not get at least 24 miles per gallon, then it is not properly tuned. b. If your car is properly tuned, then it will not get at least 24 miles per gallon. c. If your car is not properly tuned, it will not get at least 24 miles per gallon. If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function. Select one: True False Let f(x)=1-(x-3)2, evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1). Answers: (a) Answer

- Answer

2

(b) Answer

- Answer

2

(c) Answer

x2 + Answer

Which of the following will make the statement x2+3 > 1 true? Select one: a. x = -1 b. x is greater than or equal to -1 c. x > -1 d. x is less than or equal to -1

Let f(x) = 1-(x-1)2 evaluate

(a)f(2)f(3) and (b)f(23)(a)f(2)f(3) and (b)f(23)

Answers: (a) Answer (b) Answer Let f(x) = 2-x2, evaluate (a) f(x+1) and (b) f(x)+f(1). Answers: (a) f(x=1) = -x2- Answer (b) f(x) + f(1) = -x2+ Answer Find the slope of the line through (-3-1) and (x+3, y+1). Answer: Answer

x-5/x+6

From the graph shown, find: a. f(-1) b. f(0) c. 3f(2) d. the value of x that corresponds to f(x)=0 Answers: a. f(-1) = Answer b. f(0) = Answer c. 3f(2) = Answer d. x = Answer 0 Let A = {1,2,3,4,5}, B = {0,2,4,6}, and C = {-2,-1,0,1,2,3}. Which of the values of x will satisfy each statement? Select one: a. x is in A or x is in C

b. x is in A and x is in B c. x is not in B and x is in C Find the slope of the line through (0,0) and (x-1, x2-1). Answer: m = x+1 Which graph corresponds to f(x) = √x?

Which graph represents the function f(x) = {2 if x ≤ -1} {x2 if x > -1}

QUIZ 5 – Final Exam: limx→0cos2x−1cosx−1limx→0cos2x−1cosx−1

Evaluate Answer: 4

Write the contrapositive of the statement: I feel good when I jog. Answer: When I don't jog, I feel Answer: Bad

Evaluate

limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3

Answer: Answer

/ Answer

Write the negation of the statement: 8 is a prime number. Answer: 8 is Answer: not a prime number

Evaluate

limx→1x13−1x14−1limx→1x13−1x14−1

Answer: Answer

Evaluate

/ Answer

limx→103x−5−−−−−√5limx→103x−55

Answer: Answer

Every vertical line on the Cartesian plane intersects the x-axis. Select one:

True False

Evaluate

limx→43−x+5−−−−√x−4limx→43−x+5x−4

Answer: - Answer Evaluate

/ Answer

limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5

Answer: Answer Which values of x will make the statement x+5=3 or x2=9 true? Select one: a. (-2 and 3) or -3 b. -2 or (3 and -3) c. -2 and (3 or -3) d. (-2 or 3) and -3 Clear my choice

The sum of two prime numbers is a prime. False

Use the function h defined by the graph shown to determine the following limits:

limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3) (a)

Answers: (a) Answer (b) Answer

At which values of x is the function discontinuous?Answers:

f(x)=x2+x−6x−2f(x)=x2+x−6x−2continuous and

continuous at x = Answer discontinuous at x = Answer Use the function h defined by the graph below to determine the following limits:

limx→2x+h(x)limx→2x+h(x) (b) limx→3h(x2) (a)

Answers: (a) Answer (b) Answer Use the graph below to determine the right-hand limit of the function f(x) at: (a) x=-2 (b) x=10 Answers: (a) Answer (b) Answer

undefined 0

Use the functions f and g defined by the graphs as shown to determine the following limits:

limx→1(f(x)xg(x))limx→1(f(x)xg(x)) (b) limx→1f(g(x)) (a)

Answers: (a) Answer (b) Answer Use the function h defined by the graph below to determine the following limits:

limx→2(xlimx→2(x . h(x−1))h(x−1)) (b) limx→0h(3+x)−h(3)h(x) (a)

Answers: (a) Answer

(b) Answer At which values of x is the function from the graph shown continuous? State the answers from the least to the highest, if there would be more than one. Answer: x = Answer

-1

Use the function f defined by the graph shown to determine the following limits:

limx→1+f(x)limx→1+f(x) (b) limx→1−f(x) (a)

Answers: (a) Answer (b) Answer Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x2 - 2 on [0,3] Answer: Answer Use the function h defined by the graph as shown to determine the following limits:

limx→2h(2x−2)limx→2h(2x−2) (b) limx→2h(1+x) (a)

Answers: (a) Answer

1

(b) Answer

1

Use linear equation to estimate e0.06. Choose a value of 'a' to produce a small error. Note: Answers should be in decimal form. Up to two decimal places only.

e0.06 = Answer Determine all the critical points for the function.

f(x)=xex2 b. does not have any critical points Determine whether the graph is continuous or not continuous.

Answer: Not Continuous Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x5 - 3x on [1,3] Answer: There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?

x = Answer

P = Answer

additional trees

apples

Use chain rule to calculate dydxdydx of y=sin(4x3+3x+1)y=sin(4x3+3x+1) Select one: a. dydx=(12x2−3)cos(4x3+3x−1)dydx=(12x2−3)cos(4x3+3x−1)

b. dydx=(12x2+3)cos(4x3+3x+1)dydx=(12x2+3)cos(4x3+3x+1)

c. dydx=(12x2+3)cos(4x3+3x−1)dydx=(12x2+3)cos(4x3+3x−1)

d. dydx=(12x2−3)cos)4x3+3x+1)

Find a value for B so that the line y = 10x – B, goes through the point (5,-5). Answer: B = Answer For all positive real numbers a and b, if a > b, then a2 > b2 Answer: TRUE Determine whether the graph is continuous or not continuous.

Answer: Continuous Find the equation of the line tangent to the circle x2 + y2 = 25 at point (3,4). Use the general equation of the line for your final answer. Answer: 3x + Answer

y - Answer

=0

You are standing at the edge of a slow-moving river which is one mile wide and wish to return to your campground on the opposite side of the river. You can swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the campground, which is one mile from the point directly across the river from where you start your swim. What route will take the least amount of time? (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer

mi.

Shortest possible time: T ≈ Answer

hr.

Determine whether the graph is continuous or not continuous.

Answer: Not Continuous Question 14 Not yet answered Marked out of 1.00

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Question text Find an equation of the line tangent to the graph of Select one: a. y=76x−136y=76x−136

b. y=76x+136y=76x+136

c. y=136x−76y=136x−76

x2+(y−x)3=9x2+(y−x)3=9 at x=1

d. y=136x+76y=136x+76

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Question text Use linear approximations to estimate 1–√46146. Choose a value of "a" to produce a small error. Note: Answers should be in decimal form. Up to two decimal places only.

1–√46=f(146)≈L(146)146=f(146)≈L(146) = Answer Question 16

12.08

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Question text Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.

(Note: Answers should be in decimal form. Up to two decimal places only)

r ≈ Answer h ≈ Answer

V ≈ Answer

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Question text Find the slope and concavity of the graph pf x2y+y4=4+2xx2y+y4=4+2x at the point (-1,1) Select one: a. Slope = 2525, Concavity = downward

b. Slope = 5454, Concavity = downward

c. Slope = 4545, Concavity = downward

d. Slope = 4545, Concavity = upward

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Question text A container in the shape of a right circular cylinder with no top has surface area 3 ft.2 What height h and base radius r will maximize the volume of the cylinder? (Note: answers should be in decimal form. Up to two decimal places only)

r = Answer

ft.

h = Answer

ft.

V = Answer

ft3

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Question text If a and b are real numbers then (a + b)2 = a2 + b2. Select one: True False Question 20 Not yet answered Marked out of 1.00

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for cos2x+cos2y=cos(2x+2y)cos2x+cos2y=cos(2x+2y) Select one: a. y1=cosxsinx+sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx+sin(2x+2y)sin(2x+2y)−cosysiny

b. y1=cosxsinx−sin(2x+2y)sin(2x+2y)+cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)+cosysiny

c. y1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysiny

d. y1=cosxsinx+sin(2x+2y)sin(2x+2y)+cosysinyy1=cosxsinx+sin(2x+2y)sin(2x+2y)+cosysiny

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Question text Find a linear approximation to h(t)=t4−6t3+3t−7h(t)=t4−6t3+3t−7 at t=−3t=−3. (Note: Complete the linear approximation by filling in the missing numbers. Answers should be in decimal form. Up to two decimal places only)

L(t) = Answer

- Answer

(t + 3) = Answer

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Question text Find the local extreme values of the given function:

f(x)=x4−6x2f(x)=x4−6x2 Select one:

t - Answer

a. Local minimum: (1.73, -9) Local maximum: (-1.73, -9) b. Local minimum: (1.73, 9) Local maximum: (-1.73, 9) c. Local minimum: (-1.73, 9) Local maximum: (1.73, 9) d. Local minimum: (-1.73, -9) Local maximum:(1.73, -9) Clear my choice Question 23 Not yet answered Marked out of 1.00

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Question text Use chain rule to calculate dydxdydx of y = tan (e3x√)(e3x) Select one: a.

dydx=−sec2(e3x−−√)2e3x√33x−−√dydx=−sec2(e3x)2e3x33x b.

dydx=sec2(e3x−−√)2e3x√33x−−√dydx=sec2(e3x)2e3x33x c.

dydx=sec2(e3x−−√)3e3x√23x√dydx=sec2(e3x)3e3x23x

d. dydx

=−sec2(e3x−−√)3e3x√23x−−√dydx=−sec2(e3x)3e3x23x

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Question text Use chain rule to calculate dydxdydx of y=cos4(7x3)y=cos4(7x3) Select one: a. dydx=84x2cos3(7x3)sin(7x3)dydx=84x2cos3(7x3)sin(7x3)

b. dydx=−84x2cos3(7x3)+sin(7x3)dydx=−84x2cos3(7x3)+sin(7x3)

c. dydx=−84x2cos3(7x3)sin(7x3)dydx=−84x2cos3(7x3)sin(7x3)

d. dydx=84x2cos3(7x3)+sin(7x3)dydx=84x2cos3(7x3)+sin(7x3)

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Consider the function below. (\Large \lim_{x \rightarrow 3} (2x + 1) = 7 \)

What values of x guarantee that f(x) = 2x + 1 is within 0.04 units of 7? If x is within Answer units of 7.

units of 3, then f(x) is within 0.04

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Question text Find the point of intersection and the angle between x - y = 32 and 3x - 8y = 6. Answers: Point of Intersection = ( Answer Angle of Intersection = Answer Question 27 Not yet answered Marked out of 1.00

, Answer 0

)

(round-off to 2 decimal places)

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Question text If f(x) and g(x) are linear functions then f(x)g(x) is a linear function. Select one: True False Question 28 Not yet answered Marked out of 1.00

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Question text Use the function h defined by the graph below to determine the following limits:

limx→2(xlimx→2(x . h(x−1))h(x−1)) (b) limx→0h(3+x)−h(3)h(x)limx→0h(3+x)−h(3)h(x) (a)

Answers: (a) Answer (b) Answer Question 29

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Question text Determine all the critical points for the function.

f(x)=x2ln(3x)+6f(x)=x2ln(3x)+6 Select one: a. 0 b. 0.20 c. no correct answer d. 0.50 Clear my choice Question 30 Not yet answered Marked out of 1.00

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Question text Write the contrapositive of the statement: If I exercise and eat right, then I will be healthy. Don't use contractions in your answer. Answer: If I Answer Question 31 Not yet answered Marked out of 2.00

healthy, then I Answer

exercise and eat right.

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Question text Which of the following equations is the line perpendicular to 2x – 3y = 9? Select one: a. 3x + 2y =11 b. 3x – 2y = 10 c. 3x + 2y =10 d. 2x – 3y =11 Clear my choice Question 32 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 33 Not yet answered Marked out of 1.00

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Question text Given a function f, an interval [a,b] and a value V. Find a value c in the interval so that f(c)=V. Apply the Intermediate Value Theorem. NOTE: Round-off your answers to 2 decimal places, stating from the least to the highest, if there would be more than one. For positive answers, do not state the + sign anymore. For answers less than 1, precede them with 0, example 0.11

f(x)=x2f(x)=x2 on [0,3], V = 2 (b) f(x)=sinx on [0,π2],V=12f(x)=sinx on [0,π2],V=12 (a)

Answers:

(a) c = Answer

; c = Answer

(b) c = Answer Question 34 Not yet answered Marked out of 1.00

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Question text Evaluate

limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3

Answer: Answer

/ Answer

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Question text Find an equation of the line tangent to the graph of y=x2+sinπ2xy=x2+sinπ2x at x = -1 Select one: a. y = 2x - 2 b. y = -2x - 2 c. y = 2x + 2 d. y = -2x + 2 Clear my choice Question 36

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Question text Use implicit differentiation to finddydxdydx

exy=2yexy=2y Select one: a.

y1=yexy2−exxyy1=yexy2−exxy

b.

y1=yexy2−xexyy1=yexy2−xexy

c.

y1=yexy2+xexyy1=yexy2+xexy

d.

y1=yexy2+exxyy1=yexy2+exxy Clear my choice

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Answers: (a) Answer (b) Answer (c) Answer Question 38 Not yet answered Marked out of 2.00

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(Note: Answers should be in decimal form. Up to two decimal places only)

x = Answer Smallest sum:

S = Answer Question 39 Not yet answered Marked out of 1.00

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Question text What is the slope of the line through (-1,-2) and (x,y) for y = x2 + x – 2 and x=-0.98. Roundoff your answer to 2 decimal places whenever possible. Answer: slope = Answer Question 40 Not yet answered Marked out of 2.00

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Which of the following equations is the line perpendicular to 4y – 7x = 5? Select one: a. 4y – 7x + 9 = 0 b. 4x + 7y – 18 = 0 c. 4x + 7y + 18 = 0 d. 7x – 4y + 9 = 0 Clear my choice Question 41 Not yet answered Marked out of 1.00

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Consider the function below.

limx→31+x−−−−√=2limx→31+x=2 What values of x guarantee

f(x)=1+x−−−−√f(x)=1+x is within 0.0002 units

that of 2?

If x is within Answer units of 2. Question 42 Not yet answered Marked out of 3.00

units of 3, then f(x) is within 0.0002

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Question text Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only: 1. Write the equation of the line that represents the linear approximation to the function below at a given point a. f(x) = ln(1 + x); a = 0; f(0.9) y = L(x) = Answer

x

2. Use linear approximation to estimate the given function value. f(0.9) = Answer

0.9

3. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact Percent error: Answer

% 40.22

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Question text The slope of the line from point U(5,13) and the point V(x+1, x2-3) isAnswer Question 44 Not yet answered Marked out of 1.00

.

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Question text Use chain rule to calculate dydxdydx of

y=x2sec(5x)y=x2sec(5x) Select one: a. dydx

=−2xsec(5x)+5x2sec(5x)tan(5x)dydx=−2xsec(5x)+5x2sec(5x)tan(5x)

b. dydx

c. dydx

=2xsec(−5x)+5x2sec(5x)tan(5x)dydx=2xsec(−5x)+5x2sec(5x)tan(5x)

=2xsec(5x)−5x2sec(5x)tan(5x)dydx=2xsec(5x)−5x2sec(5x)tan(5x)

d. dydx

=2xsec(5x)+5x2sec(5x)tan(5x)dydx=2xsec(5x)+5x2sec(5x)tan(5x)

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Let f(x) = (x-1)2 and define S(x) to be the slope of the line through the point (0,0) and (x,f(x)). Evaluate S(6). Answer: S(6) =Answer (Use fractional answer when possible, say 12/13. Do not use space between symbol and number.) Question 46 Not yet answered Marked out of 3.00

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(Note: Answers should be in decimal form only. Up to two decimal places}

x ≈ Answer

ft.

y ≈ Answer

ft.

L ≈ Answer

ft.

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Question text Evaluate

limx→0(x+1)3−1xlimx→0(x+1)3−1x

Answer: Answer Question 48 Not yet answered Marked out of 3.00

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Question text Fill in the missing the numbers to find the correct answer/s: Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.

P = xy

2

Answers:

x = Answer y = Answer P = Answer Question 49 Not yet answered Marked out of 1.00

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Question text If f(x) and g(x) are linear functions, then f(x) + g(x) is a linear function. Select one: True False Question 50 Not yet answered Marked out of 1.00

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Question text Use Newton's Method to find the root of 2x2+5=ex2x2+5=ex accurate to six decimal places in the interval [3,4]. (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer Question 51 Not yet answered Marked out of 2.00

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(Note: Answer should be in decimal form. Up to two decimal places only)

x ≈ Answer

ft.

θ = Answer

degrees.

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Question text A hotel charges Php1,500 per night for a room during the tourist season from June 1 through September 15, and Php1,200 per night otherwise. Define a multiline function which describes these rates. f(x) is the cost for one night on date x . Choose from the options. Select one:

a.

b.

c. Clear my choice Question 53 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice

Question 54 Not yet answered Marked out of 1.00

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Consider the function below.

limx→24x−3=5limx→24x−3=5 What values of x guarantee that f(x) = 4x - 3 is within 1 unit of 5? Select one: a. If x is within 2.25 units distance of 2, then f(x) is within 1 unit of 5. b. If x is within 1.75 units distance of 2, then f(x) is within 1 unit of 5. c. If x is within 0.25 unit distance of 2, then f(x) is within 1 unit of 5. d. If x is within 2 units distance of 2, then f(x) is within 1 unit of 5. Clear my choice Question 55 Not yet answered Marked out of 2.00

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(Note: Answers should be in decimal form only. Up to two decimal places only)

x = Answer y = Answer

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Consider the function below.

limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5?

Select one: a. If x is within 0.98 unit distance of 1, then f(x) is within 0.05 unit of 5. b. If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5. c. If x is within 1.02 units distance of 1, then f(x) is within 0.05 unit of 5. d. If x is within 1 unit distance of 1, then f(x) is within 0.05 unit of 5. Clear my choice Question 57 Not yet answered Marked out of 1.00

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Question text Determine all the critical points for the function

y=6x−4cos(3x)y=6x−4cos(3x) x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,... x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,...

Select one: a. 1.2217; 1.9199 b. 1.2217; 0.9199 c. 1.7991; 1.2217 d. 1.1991; 1.7122 Clear my choice Question 58 Not yet answered

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for x−y3y+x2 Select one: a. y1=1−y+3x2−4x3y2+x−2y1=1−y+3x2−4x3y2+x−2

b. y1=1−y−3x2−4x3y2−x+2y1=1−y−3x2−4x3y2−x+2

c. y1=1−y−3x2−4x3y2+x+2y1=1−y−3x2−4x3y2+x+2

d. y1=1−y+3x2−4x3y2+x+2y1=1−y+3x2−4x3y2+x+2

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Question text Evaluate

limx→0(x+5)2−25xlimx→0(x+5)2−25x

Answer: Answer Question 60 Not yet answered

=x+2x−y3y+x2=x+2

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Question text Evaluate

limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5

Answer: Answer Question 61 Not yet answered Marked out of 3.00

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Question text Do the following. Type your answer on the space/s provided. Up to two decimal places only. 1. Write the equation of the line that represents the linear approximation to the function below at the given point a.

f(x)=e2;a=0;f(0.05)f(x)=e2;a=0;f(0.05)

f(a) = Answer

7.39

2. Use the linear approximation to estimate the given function value.

f(0.05) ≈ L (0.05) = Answer

0.05

3. Compute the percent error in your approximation.

Percent error ≈ Answer Question 62 Not yet answered Marked out of 2.00

%

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Given f(x) = 2x + 3 and g(x) = x2. Evaluate . Sample text answer: 3x^2+6x7. Do not use space between the number, letter and symbol. Answer:Answer Question 63 Not yet answered Marked out of 1.00

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Question text Use Newton's Method to determine x2x2 for f(x)=xcos(x)−x2f(x)=xcos(x)−x2 if x0=1x0=1 (Note: Answers should be in decimal form. Up to two decimal places only.)

x2 = Answer Question 64 Not yet answered Marked out of 1.00

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for (x−y)2=x+y−1(x−y)2=x+y−1 Select one:

a. y1=2y−2x+12y−2x−1y1=2y−2x+12y−2x−1

b. y1=2y−2x+12y+2x−1y1=2y−2x+12y+2x−1

c. y1=2y+2x−12y+2x+1y1=2y+2x−12y+2x+1

d. y1=2y+2x−12y−2x+1y1=2y+2x−12y−2x+1

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Question text Use chain rule to calculate dydxdydx of

y=e−x2y=e−x2 Select one: a. dydx

=2x−x2dydx=2x−x2

b. dydx

=−2x−x2dydx=−2x−x2

c. dydx

=2xx2dydx=2xx2

d. dydx

=−2xx2dydx=−2xx2

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Question text Locate the critical points of the following functions. Then use the second derivative test to determine whether they correspond to local minima or local maxima or whether the test is inconclusive.

p(x)=x−4x2+20p(x)=x−4x2+20 Select one: a. Critical points: (1, -1/4) and (2, -1/20) Local minimum: x = -2 Local maximum: x = 5 b. Critical points: (2, -3/4) and (10, -1/20) Local minimum: x = -20 Local maximum: x = 1 c. Critical points: (2, -1/4) and (10, -1/2) Local minimum: x = 2 Local maximum: x = 10

d. Critical points: (2, -1/4) and (10, -1/20) Local minimum: x = -2 Local maximum: x = 10 Clear my choice Question 67 Not yet answered Marked out of 1.00

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Question text Use Newton's Method to find the root of x4−5x3+9x+3=0x4−5x3+9x+3=0 accurate to six decimal places in the interval [4,6]. (Note: Answers should be in decimal form. Up to two decimal places only.)

x ≈ Answer Question 68 Not yet answered Marked out of 1.00

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Identify the absolute extrema and relative extrama for the following function.

f(x)=x3f(x)=x3 on [-2,2] Select one:

a. The function has an absolute maximum of 8 at x = 0 and absolute minimum of -8 at x = 1. The function has a no relative extrema. b. The function has an absolute maximum of -8 at x = 2 and absolute minimum of 8 at x = 2. The function has no relative extrema. c. The function has an absolute maximum of 8 at x = 2 and absolute minimum of -8 at x = 2. The function has no relative extrema. d. The function has an absolute maximum of 8 at x = -2 and absolute minimum of -8 at x = 2. The function has a relative minimum of (0,0) and no relative maxmum. Clear my choice Question 69 Not yet answered Marked out of 1.00

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Question text Use the functions f and g defined by the graphs as shown to determine the following limits:

limx→1f(x)+g(x)limx→1f(x)+g(x) (b) limx→2f(x)g(x)limx→2f(x)g(x) (a)

Answers: (a) Answer

(b) Answer Question 70 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 71 Not yet answered Marked out of 1.00

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Question text Use implicit differentiation to find dydxdydx

(xy+1)3=x−y2+8(xy+1)3=x−y2+8 Select one: a.

y1=1−3y(xy+1)23x(xy+1)2+2yy1=1−3y(xy+1)23x(xy+1)2+2y

b.

y1=1+3y(xy+1)23x(xy+1)2−2yy1=1+3y(xy+1)23x(xy+1)2−2y

c.

y1=2y+2x−12y−2x+1y1=2y+2x−12y−2x+1

d.

y1=1+3y(xy+1)23x(xy+1)2+2yy1=1+3y(xy+1)23x(xy+1)2+2y Clear my choice

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Question text Evaluate

limx→7x−3−−−−√limx→7x−3

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Question text Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen? (Note: Answers should be in decimal form. Up to two decimal places only)

x = Answer y = Answer A = Answer

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ft. ft. ft2

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Question text For the function

f(x)=x(x2+1)2f(x)=x(x2+1)2 on [-2,2] Find the critical points and the absolute extreme values of f on the given interval. Select one: a. x=±23−−√x=±23 as the critical points absolute maximum value of f: −33√16−3316 absolute minimum value of f: 33√163316

b. x=13−−√x=13 as the critical points absolute maximum value of f: −33√16−3316 absolute minimum value of f: −33√16−3316

c. x=±13−−√x=±13 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:33√163316

d. x=±12−−√x=±12 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:: 33√163316

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for y=x2y3+x3y2y=x2y3+x3y2 Select one: a. y1=2xy3+3x2y21+3x2y2+2x3yy1=2xy3+3x2y21+3x2y2+2x3y

b. y1=2xy3+3x2y21−3x2y2+2x3yy1=2xy3+3x2y21−3x2y2+2x3y

c. y1=2xy3+3x2y21−3x2y2−2x3yy1=2xy3+3x2y21−3x2y2−2x3y

d. y1=2xy3+3x2y21+3x2y2−2x3yy1=2xy3+3x2y21+3x2y2−2x3y

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Question text

Consider the function below.

limx→13x+2=5limx→13x+2=5

What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5? Select one: a. If x is within 1.02 units distance of 1, then f(x) is within 0.05 unit of 5. b. If x is within 0.98 unit distance of 1, then f(x) is within 0.05 unit of 5. c. If x is within 1 unit distance of 1, then f(x) is within 0.05 unit of 5. d. If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5. Clear my choice Question 77 Not yet answered Marked out of 3.00

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Question text An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions will result in a box with the largest possible volume?

Answers:

x = Answer

ft.

y = Answer

ft.

V = Answer

ft.3

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Question text Write the negation for the statement: All quadratic equations have solutions. Answer: Answer

all quadratic equations Answer

solutions.

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Question text Use the function h defined by the graph shown to determine the following limits:

limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3)limx→0h(3+x)−h(3) (a)

Answers: (a) Answer (b) Answer Question 80 Not yet answered Marked out of 1.00

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Question text Use implicit differentiation to find dydxdydx,

x3=x+yx−yx3=x+yx−y Select one: a.

y1=3x2(x−y)2+2y2xy1=3x2(x−y)2+2y2x

b.

y1=3x2(x−y)2−2y2xy1=3x2(x−y)2−2y2x

c.

y1=3x2(x+y)2+2y2xy1=3x2(x+y)2+2y2x

d.

y1=3x2(x+y)2−2y2xy1=3x2(x+y)2−2y2x Clear my choice

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Question text Find the point of intersection and the angle between y = 4 - 2x and x - y = -1. Answers: Point of Intersection = ( Answer Angle of Intersection = Answer

, Answer 0

)

(round-off to 2 decimal places)

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Question text Find a linear approximation of f(x)=3xe2x−10f(x)=3xe2x−10 at x = 5. (Note: Fill in the missing numbers to get the get the correct answer. Answers should be in decimal form. Up to two decimal places only.) L(x) = Answer Question 83 Not yet answered

+ Answer

(x - 5) = Answer

x + Answer

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 84 Not yet answered Marked out of 3.00

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Question text Find the point of intersection and the angle between 2x - 3y = 3 and 4x - 2y = 10. Answers:

Point of Intersection = ( Answer Angle of Intersection = Answer

, Answer 0

)

(round-off to 2 decimal places)

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Question text Which of the following is the appropriate multiline function for the graph shown?

Select one:

a.

b. c. Last option napicture Clear my choice Question 86 Not yet answered Marked out of 3.00

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Question text Consider a rectangle of perimeter 12 inches. Form a cylinder by revolving this rectangle about one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume? (Note: Answer should be in decimal form. Up to two decimal places only)

r = Answer

ft

h = Answer

ft

V ≈ Answer

ft3

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Question text Evaluate

limx→43−x+5−−−−√x−4limx→43−x+5x−4

Answer: - Answer

/ Answer

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Question text Use chain rule to calculate dydxdydx of

y=(5x2+11x)20y=(5x2+11x)20 Select one: a. dydx=(−20)(5x2+11x)19(10x+11)dydx=(−20)(5x2+11x)19(10x+11)

b. dydx=(20)(5x2+11x)19(10x+11)dydx=(20)(5x2+11x)19(10x+11)

c. dydx=(20)(5x2+11x)19(10x−11)dydx=(20)(5x2+11x)19(10x−11)

d. dydx=(−20)(5x2+11x)19(10x−11)dydx=(−20)(5x2+11x)19(10x−11)

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Not Continuous b. Continuous Clear my choice Question 90 Not yet answered Marked out of 1.00

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Question text Evaluate

limx→103x−5−−−−−√5limx→103x−55

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Question text Which of the following are integer values of x that will make the statement x>4 and x<9 true? Select one or more: a. 9 b. 8 c. 5 d. 4 e. 6 f. 7 Question 92 Not yet answered Marked out of 1.00

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Question text Determine whether the graph is continuous or not continuous.

Select one: a. Continuous b. Not Continuous Clear my choice Question 93 Not yet answered Marked out of 1.00

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Question text If x divides 49, then x divides 30. Select one: True False Question 94 Not yet answered Marked out of 1.00

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Question text Every straight line on the Cartesian plane intersects the x-axis. Select one: True False Question 95 Not yet answered Marked out of 1.00

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Question text Assume that y is a function of x. Find y1=dydxy1=dydx for y=sin(3x+4y)y=sin(3x+4y) Select one: a.

y1=3cos(3x+4y)1−4cos(3x+4y)y1=3cos(3x+4y)1−4cos(3x+4y)

b.

y1=3cos(3x+4y)1+4cos(3x+4y)y1=3cos(3x+4y)1+4cos(3x+4y)

c.

y1=3cos(3x−4y)1+4cos(3x−4y)y1=3cos(3x−4y)1+4cos(3x−4y)

d.

y1=3cos(3x−4y)1−4cos(3x−4y)y1=3cos(3x−4y)1−4cos(3x−4y) Clear my choice

Question 96

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Question text Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only: 1. Write the equation of the line that represents the linear approximation to the function below at the given point a: f(x) = 12 - x2 ; a = 2 ; f(2.1) Answer: y = L(x) = Answer

x + Answer

2. Use linear approximation to estimate the given function value. f(2.1) = Answer 3. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact Percent error is: Answer

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Question text

%

(Note: Answers should be in decimal form. Up to two decimal places only)

Largest possible slope: x = Answer y = Answer S = Answer Smallest possible slope: x = Answer y = Answer S = Answer Question 98 Not yet answered Marked out of 1.00

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Question text

Find an equation of the line tangent to the graph of (x2+y2)3=8x2y2(x2+y2)3=8x2y2 at the point (-1,1) Select one: a. y - 1 = x + 2 b. y - 1 = x - 2 c. y + 1 = x - 2 d. y + 1 = x + 2 Clear my choice Question 99 Not yet answered Marked out of 5.00

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Question text A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. Given that variable x shall be the length of one edge of the square cu from each corner of the sheet of cardboard, what will be the dimensions of the box with largest volume? (Note: Answer should be in decimal form and up to two decimal places only)

x ≈ Answer

ft, so

Length = Answer Width = Answer

ft

Height = Answer V ≈ Answer

ft

ft

ft3

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Question text Given f(x) = 2x + 3. Evaluate (f°f)(x). Sample text answer: 3x^2+6x-7. Do not use space between the number, letter and symbol. Answer:Answer