Exit Reviewer

REVIEWER 1.) The area bounded the curve y= 2x+1, from x=0 to x=4. a.) 19 b.) 18 c.) 20 d.) 16 0.4

2.) Approximate the integral to the 5th decimal place. ∫0 √1 + 𝑥 4 . a.) 0.20051 b.) 0.80204 c.) 0.40102 d.) 0.10026 𝜋 2 𝜋 4

3.) Evaluate the integral ∫ 𝑐𝑜𝑠𝑥 𝑑𝑥. a.) 0.329 b.) 0.293 c.) 0.923 d.)423 𝑑𝑓

4.) Given the function f (x,y,z)= xcosz + x2y3ez, determine 𝑑𝑦. a.) 3x2y2e2 b.) 3y2 c.) cos2+2xy3ez d.) -sinz2+x2y3ez. 5.) At which value of x does the limit of the function exists. a.) None of the above b.) 5 c.) 2 d.) 0 6.) A rectangular field is to be enclosed by a fence & divided into 3 lots by fences parallel to one of the sides. Find the dimension of the largest field that can be enclosed with 800 feet of fencing. a.) 100ft x 200ft b.) 50ft x 400ft c.) 75ft x 75ft d.) 80ft x 100ft 7.) A lot in the shape of a quadrant of a circle of radius 100m. Find the area of the largest rectangular building that can be constructed inside the lot. a.) 8000 b.) 6000 c.) 5000 d.) 7000 8.) A triangle has a base of 12ft long and an altitude of 8ft high. Find the area of the largest rectangle in ft2 that can be inscribed in a triangle so that the base of the rectangle falls on the base of the triangle. a.) 26 b.) 28 c.) 24 d.) 30 9.) Find the area of the triangle in 3-space between (1,0,0) (0,1,0) and (0,0,1). a.) √2/3 b.) 3/2 c.) 2/3 d.) √3/2 10.) Find the derivative of y=5-1/x. −

a.)

1

5 𝑥 (𝑙𝑛5)𝑥 𝑒

−

b.)

1

5 𝑥 𝑥2

1

c.)

− 5 𝑥 (𝑙𝑛5) 𝑥2

d.) 5−1/𝑥 𝑙𝑛5𝑥 2

11.) Find the partial derivative of x2+3xy-4y2 with respect to x. a.) 3x-8y b.) 8+xy c.) x+y d.) 2x+3y 12.) Given the function f(x,y)= 4x4y2-10xy3+y, find fxy. a.) 8x4y-30xy+1 b.) 48x2y2 c.) 16x4y-60xy d.) 32x3y-30y2 13.) 2 automobiles start from the point A at the same time. One travels west at 60 miles/h and the other travels north 35mi/h. How fast is the distance net them changing 3 hours later? a.) 69.46 b.) 65.46 c.) 72.56 d.) 57.46

REVIEWER 1

14.) Find the point of inflection of the curve y= x2-𝑥. a) (3,0)

b.) (2,0)

c.) (4,0)

d.) (1,0)

15.) Two posts, one 8 meters high and the other 12 m high, stand 15 m apart. They are to be stayed by wires by wires attached to a single stake at the ground level, the wires running to the tops of the parts. How far from the post should the shorter post should stake be placed to used the least amount of wire? a.) 6 b.) 4 c.) 3 d.) 5 tan 𝑥 . 𝑛→∞ 𝑥

16.) Evaluate lim a.) e

b.) 0

c.) ∞

d.) 1

17.) Find the maximum area of an isosceles triangle whose perimeter is 18in. a.) 56.45 in2 b.) 34.56 in2 c.) 15.59 in2 d.) 25.25 in2 18.) Find a unit vector that has the same direction as (-3i + 7j). 3 7 3 7 −3 a.) 𝑖− 𝑗 b.) -√58 𝑖 + 7 𝑗 c.) 𝑖 − 𝑗 d.) 𝑖 + √58

√58

√50

√58

√58

7 √58

𝑗

19.) Determine the equation of the plane that contains the points P= (1,-2,0) Q=(3,1,4) R=(0,-1,2). a.) 5x-2y+8z= 16 b.) 8x-2y+5z= 18 c.) 5x-20y+8z= 18 d.) 2x-8y+5z= 18 20.) Find an equation of the plane through the origin parallel to the plane 2x-y+3z=1. a.) 2x-y+3z=0 b.) x-2y+3z=0 c.) any of these d.) 3x-2y+2=0 21.) Which of the following vectors are neither parallel nor orthogonal? a.) <-5,3,7> & <6, -8, 2> b.) -i+2j+5k & 3i+4j-k c.) none of the above d.) 2i+6j-4k & -3i 9j+6k 22.) Find the bounded area by the parabolas y= 6x-x2 & y=x2-2x. Take note that parabolas intersection at (0,0) (4,8). a.) 64/3 b.) 54/3 c.) 74/3 d.) 44/3 23.) If A∙B= 0. What is angle between vector A & B. a.) 𝜋 /4 b.) 𝜋 c.) 𝜋/3 d.) 𝜋/2 24.) Find the angle between the two vectors. A= 2i+3j+4k ; u= <2,3,4> B= i-2j+3k ; v= <1,-2,3> a.) 88.6 deg

b.) 66.6 deg c.) 68.6 deg

25.) Which of the following is a vector. a.) None b.) wind due to typhoon Egay d.) cost of a train ticket 26.) Find the sum of the vectors <-1,4> & <6,-2>.

d.)86.6 deg

c.) population of Batch 2018 students in MU

REVIEWER a.) <-5.2>

b.) <5,2>

c.) <2,5>

d.) <2-5,>

27.) Find a distance between plane 2x+4y-6=0 and point m (0,3,6). a.) 2 b.) 3 c.) 4 d.) 1

28.) Which of the following series is/are convergent. ∞

1 𝐼. ∑ 𝑛 + 3𝑛 𝑛=1

a.) II only b.) III only

c.) I only

∞

𝑛 𝐼𝐼. ∑ 𝑛+2 𝑛=1

∞

𝐼𝐼𝐼. ∑ 𝑘 2 𝑒 −𝑘 𝑘=1

d.) I and III

29.) Calculate the angle between the two planes by the equation 2x+4y-2z=5 and 6x-8y-2z=14. a.) 73.12 deg b.) 71.32 deg c.) 74.12 deg d.) 72.61 deg 30.) Calculate the cross product between A= 3i-3j+k and B= 4i+9j+2k. a.) -15i +2j -39k b.) -15i-2j+39k c.) -2i-25j+39k d.) -39-15j+2k 1

31.) Find the scalar projection of b= j+2 𝑘 to a= 2i-j+4k. a.)

√5 2

b.)

1 √21

c.)

−1 √21

d.)

2 √5

32.) Suppose B= 2i+2j+k. Suppose also that B makes an angle of 30o? a.)

3 √3

b.)

1 √3

c.)

2 √3

d.)

4 √3

33.) At a given instant, the legs of a right triangle are 16 inches and 12 inches, respectively. The first leg decreases at 0.5 in/min and the second leg increases of 2 in/min. At what rate is the area increasing after 2 mins?