Calculus 2 Questions

MA 312 - Section Number _________ Final Exam Name__________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the integral.

1) (8x2 + x-3) dx 1)

A) 8x3

3 +

x-2 2

+ C B) - 8x3

3 +

x-2 2

+ C

C) - 8x3

3 -

x-2 2

+ C D) 8x3

3 -

x-2 2

+ C

2) te-7t2 dt 2)

A) 1 14

e-7t2 + C B) 1 7

e-7t2 + C C) - 1 7

e-7t2 + C D) - 1 14

e-7t2 + C

Find the area between the curves. 3) y = x2, y = 4 3)

A) 32 3

B) 31 3

C) 34 3

D) 37 3

Use integration by parts to find the integral. Round the answer to two decimal places if necessary.

4) 1

0

x x + 1

dx 4)

A) -1.33 B) -2.27 C) 0.39 D) -0.94

Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral.

5) 1

x2 - 49 dx 5)

A) 1 14

ln x - 7 x + 7

+ C B) 1 14

ln 7 + x 7 - x

+ C

C) ln x + x2 - 49 + C D) ln x + x2 + 49 + C

Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by the curves. 6) f(x) = 3x + 2 , y = 0, x = 1, x = 5 6)

A) 44 B) 44 C) 80 D) 80

Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.

7) 1

5 8x(x + 1)2

dx 7)

A) -0.746 B) -5.965 C) 0.625 D) 0.120

1

Find the partial derivative.

8) Let z = g(x,y) = 9x + 7x2y2 - 4y2. Find z y

. 8)

A) 14xy2 - 8y B) 9 + 14xy2 C) 14x2y - 8y D) 9 + 14x2y

Find the indicated relative minimum or maximum. 9) Minimum of f(x,y) = x2 - 14x + y2 - 16y,

subject to 2x + 3y = 12 9)

A) f(1, 5) = -68 B) f(3, 2) = -61 C) f(2, 0) = -24 D) f(0, 1) = -15

Evaluate the iterated integral.

10) 2

0

5

0 (9x2y + 5xy) dy dx 10)

A) 85 2

B) 85 C) 425 2

D) 425

Find the expected value of the probability density function to the nearest hundredth.

11) f(x) = 1 - 1 x

; [1, 4] 11)

A) 2.83 B) 2.67 C) 3.00 D) 2.50

Find all local extreme values of the given function and identify each as a local maximum, local minimum, or saddle point. 12) f(x, y) = 4 - x4y4 12)

A) f(4, 4) = -65,532, local minimum B) f(0, 0) = 4, local maximum; f(4, 4) = -65,532, local minimum C) f(4, 0) = 4, saddle point; f(0, 4) = 4, saddle point D) f(0, 0) = 4, local maximum

Evaluate the integral.

13) /12

- /12 tan4 3t dt 13)

A) 9

- 2 9

B) - 4 9

C) 6

- 4 9

D) 6

Find the sum of the series as a function of x.

14) n=1

(x + 8)n 14)

A) - x + 8 x + 9

B) - x + 8 x + 7

C) x + 8 x + 9

D) x + 8 x + 7

2

Find the derivative. 15) s = t5 - csc t + 18 15)

A) ds dt

= 5t4 + csc t cot t B) ds dt

= t4 - cot2t + 18

C) ds dt

= 5t4 - csc t cot t D) ds dt

= 5t4 + cot2t

Find the Taylor series generated by f at x = a. 16) f(x) = x3 - 5x2 + 10x - 10, a = 5 16)

A) (x - 5)3 - 10(x - 5)2 + 15(x - 5) - 40 B) (x - 5)3 + 10(x - 5)2 + 15(x - 5) + 40 C) (x - 5)3 - 10(x - 5)2 + 35(x - 5) - 40 D) (x - 5)3 + 10(x - 5)2 + 35(x - 5) + 40

3