Calculus-quiz1-finals-version-2.pdf

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

10

feet/second

-20

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

-1.67

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

7.5

(b) A(4) - A(1) = Answer

square units 9

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

1

g(-1) = Answer h(4) = Answer

-2 1

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

2

and g(2n+1) =Answer

1+(2/n)

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

-7

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

1

6x+3A+2 6x+A+4

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

9

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

3x-10 3x-6

-1/5 -3

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

x+1

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

5 2 1

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

-1 1

0 1

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

Answers: f(-1) = Answer -2f(1) = Answer

-1 6

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

-2

3

or and x = Answer

-3

) <--- 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.) 5.97

Slope at x=2.97 = Answer

6.00

Slope at x=3.001 = Answer Slope at x=3+h = Answer

6+h

6

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: 4.99

when x=1.99: m = Answer when x=2.004: m = Answer when x=2+h:m = Answer

5.00

Round-off your answer to 2 decimal places. Round-off your answers to 3 decimal places.

5+h

when h approaches 0: m = Answer

5

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:

20.1

when x=-0.90: m = Answer

3.3

when x=-1.05: m = Answer

h^2+1

when x=h-1: m = Answer

/h

when h approaches 0: m = Answer

1

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 (b) V = Answer (c) V = Answer

15

ft/sec

-5

ft/sec

20

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

4

square units

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

6

A(3) = Answer

7.5

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

400

Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3. Answer: If x = - Answer

2

and x = Answer

3

then x2 + x - 6 is not equal to 0

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

x-5

.

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

5/2

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

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

<=

3.

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 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

1

- Answer

x

(b) Answer

1

- Answer

x

(c) Answer

-4

x2 + Answer

2

2

8x-3

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) Answer

0

(b) Answer

8/9

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

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

2x+1

(b) f(x) + f(1) = -x2+ Answer

3

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

2 1

-14

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

108

/ Answer

7

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

4

/ Answer

3

limx→103x−5−−−−−√5limx→103x−55

Answer: Answer

1

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 1

Answer: - Answer Evaluate

/ Answer

6

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

Answer: Answer

2

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

1

(b) Answer

-2

At which values of x is the function discontinuous?Answers: continuous at x = Answer

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

-3

discontinuous at x = Answer

2

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

3

(b) Answer

3/4

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

0

(b) Answer

5/4

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. 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

2

(b) Answer

-1

If x divides 49, then x divides 30. =false For all positive real numbers a and b, if a > b, then a2 > b2. =false If f(x) and g(x) are linear functions then f(x)g(x) is a linear function. =true 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

1.4

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

1.06

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

15

P = Answer

42250

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

55

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

0.89

mi.

Shortest possible time: T ≈ Answer

0.71

hr.

Determine whether the graph is continuous or not continuous.

Answer: Not Continuous

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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

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Question text

x2+(y−x)3=9x2+(y−x)3=9 at x=1

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

1.89

h ≈ Answer

2.67

V ≈ Answer

9.93

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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

1

ft.

h = Answer

1

V = Answer

3.14

ft.

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

227

- Answer

267

(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

-267

t - Answer

574

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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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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.

0.02

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

50

Angle of Intersection = Answer

-24.44

, Answer 0

18

)

(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

8/3

(b) Answer

-6/5

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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

am not

healthy, then I Answer

do not

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

-1.41

(b) c = Answer

0.52

; c = Answer

1.41

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Question text Evaluate

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

Answer: Answer Question 35 Not yet answered Marked out of 1.00

108

/ Answer

7

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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

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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

1.5

Smallest sum:

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

8.5

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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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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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Question text

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.

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

x

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

0.9

0.9

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

40

% 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

x+4

.

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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

=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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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). 25/6

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

8.77

y ≈ Answer

16.67

ft.

L ≈ Answer

17.64

ft.

ft.

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Question text Evaluate

limx→0(x+1)3−1xlimx→0(x+1)3−1x

Answer: Answer

3

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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

3

y = Answer

6

P = Answer

108

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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

4.36

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Question text

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

x ≈ Answer

17.32

θ = Answer

30

ft.

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 Question 55 Not yet answered Marked out of 2.00

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Question text

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

x = Answer

3.50

y = Answer

1.87

Question 56 Not yet answered Marked out of 2.00

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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 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

=x+2x−y3y+x2=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

10

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Question text Evaluate

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

Answer: Answer Question 61 Not yet answered

2

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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

20

%

Question 62 Not yet answered Marked out of 2.00

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Question text

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

4x^2+12x+9

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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

0.74

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

4.53

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Question text

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

2

(b) Answer

4/3

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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

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Question text Evaluate

limx→7x−3−−−−√limx→7x−3

Answer: Answer Question 73 Not yet answered Marked out of 3.00

2

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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

50

ft.

y = Answer

125

A = Answer

6250

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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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

4

ft.

y = Answer

2

ft.

V = Answer

32

ft.3

Question 78 Not yet answered Marked out of 1.00

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

not

all quadratic equations Answer

all

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

3

(b) Answer

3/4

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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

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Question text Find the point of intersection and the angle between y = 4 - 2x and x - y = -1. Answers: 1

Point of Intersection = ( Answer Angle of Intersection = Answer

, Answer

-71.56

0

2

)

(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

15

+ Answer

33

(x - 5) = Answer

33

x + Answer

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

150

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

3

Angle of Intersection = Answer

29.74

Question 85 Not yet answered Marked out of 3.00

, Answer 0

1

)

(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

4

ft

h = Answer

2

V ≈ Answer

100.53

ft

ft3

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Question text Evaluate

limx→43−x+5−−−−√x−4limx→43−x+5x−4

Answer: - Answer Question 88 Not yet answered

1

/ Answer

6

Marked out of 1.00

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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

Answer: Answer

1

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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

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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)

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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

-4

x + Answer

16

2. Use linear approximation to estimate the given function value. f(2.1) = Answer

7.6

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

0.13

%

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Question text

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

Largest possible slope: x = Answer

1

y = Answer

1.5

S = Answer

-0.75

Smallest possible slope: x = Answer

-1

y = Answer

-1.5

S = Answer

0.75

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

0.57

ft, so

Length = Answer Width = Answer

1.86

Height = Answer V ≈ Answer

3.03

ft

2.86

0.57

ft ft

ft3

Question 100 Not yet answered Marked out of 2.00

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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

4x+9