MA102-FinalExam-Answers

When approximating the area under the curve

on the interval

, using the midpoint rule over four subintervals, one would obtain which of the following?

Choose one answer.

	A. 20
	B.
	C. 66
	D.
	E. None of the above

Question 2

To numerically approximate solutions to differential equations, it is common to use which of the following?

Choose one answer.

	A. Simpson's Rule
	B. Rolle's Method
	C. Newton's Method
	D. Euler's Method
	E. None of the above

Question 3

Find the length of the curve

over the interval

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 4

What integral could you use to find the length of the curve

over the interval

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 5

Find the area between the curves

, and

Choose one answer.

	A. 18.5
	B. 19.5
	C. 20.5
	D. 21.5
	E. None of the above

Question 6

Find the area between the curves

and

from

Choose one answer.

	A.
	B.
	C. 4
	D.
	E. None of the above

Question 7

Find the area between the curves

and

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 8

Find the average value of the function

on the interval

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 9

Find the average value of the function

on the interval

Choose one answer.

	A. 1
	B.
	C. 2
	D. 3
	E. None of the above

Question 10

If possible, find the sum of the series

Choose one answer.

	A.
	B.
	C.
	D. 3
	E. The series diverges.

Question 11

If possible, find the sum of the series

Choose one answer.

	A.
	B.
	C.
	D.
	E. The series diverges.

Question 12

If possible, find the sum of the series

Choose one answer.

	A. 3
	B.
	C. 4
	D.
	E. The series diverges.

Question 13

If possible, find the sum of the series

Choose one answer.

	A.
	B.
	C. 1
	D. 2
	E. The series diverges.

Question 14

Let

. Which of the following is NOT necessary to use the integral test to check the convergence or divergence of

? Choose the best answer.

Choose one answer.

	A. is continuous.
	B. is concave up.
	C. is decreasing.
	D. is positive.
	E. All of the above

Question 15

Which of the following best describes the series

Choose one answer.

	A. The sequence converges conditionally.
	B. The sequence converges absolutely.
	C. The sequence diverges.
	D. All of the above

Question 16

Which of the following best describes the series

Choose one answer.

	A. The sequence converges conditionally.
	B. The sequence converges absolutely.
	C. The sequence diverges.
	D. All of the above

Question 17

Which of the following best describes the series

Choose one answer.

	A. The sequence converges conditionally.
	B. The sequence converges absolutely.
	C. The sequence diverges.
	D. All of the above

Question 18

If the acceleration of a particle with initial velocity

is given by

, how far is it from its initial position at time

Choose one answer.

	A. 41
	B. 42.5
	C. 45
	D. 48.75
	E. None of the above

Question 19

If the acceleration of a particle with initial velocity

is given by

, then how far is it from its initial position at time

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 20

Calculate

Choose one answer.

	A. 1
	B.
	C.
	D.
	E. None of the above

Question 21

Calculate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 22

Find

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 23

The Fundamental Theorem of Calculus states which of the following?

Choose one answer.

	A. If is differentiable at , then .
	B. If is differentiable on (a,b), then there exists in the interval such that .
	C. If has a local max at , then or is undefined.
	D. If , then .
	E. None of the above

Question 24

To find the interval on which

is concave upward, an immediate application of which theorem will simplify the problem?

Choose one answer.

	A. L’Hopital’s Rule
	B. Mean Value Theorem
	C. Descartes’ Rule of Signs
	D. Second Fundamental Theorem of Calculus
	E. None of the above

Question 25

The growth rate of a population of bacteria is proportional to the current population. If the initial population was 2000 bacteria and the population after 1 day was 40,000 bacteria, how many bacteria would one expect to find at the end of 2 days?

Choose one answer.

	A. 80,000 bacteria
	B. 400,000 bacteria
	C. 800,000 bacteria
	D. 2,000,000 bacteria
	E. None of the above

Question 26

The half-life of Polonium is 102 years. If a 3kg sample now weighs .375 kg, how many years have passed?

Choose one answer.

	A. 102 years
	B. 204 years
	C. 306 years
	D. 408 years
	E. None of the above

Question 27

The half-life of Californium is about 900 years. What equation models the amount remaining from a 400g sample after

years?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 28

Calculate

Choose one answer.

	A. 0
	B.
	C. 1
	D.
	E. None of the above

Question 29

Calculate

Choose one answer.

	A. 0
	B.
	C. 1
	D.
	E. None of the above

Question 30

Consider the integral

. Which of the following is a correct characterization of this integral?

Choose one answer.

	A. The integral is undefined, if and .
	B. The integral is undefined, if , , and .
	C. The integral is undefined, only if or .
	D. The integral is undefined, only if or is an integer multiple of .
	E. The integral is defined for all finite values of and .

Question 31

For what values of

is the following integral convergent:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 32

Evaluate the following integral:

Choose one answer.

	A. 0
	B.
	C.
	D. 1
	E. The integral diverges.

Question 33

Evaluate the following integral:

Choose one answer.

	A. 0
	B. 1
	C.
	D.
	E. None of the above

Question 34

Evaluate the following integral:

Choose one answer.

	A. 0
	B.
	C.
	D.
	E. The integral diverges.

Question 35

Evaluate the following integral:

Choose one answer.

	A. 0
	B.
	C. 1
	D.
	E. The integral diverges.

Question 36

and

, where both series have only positive terms, which of the following is false?

Choose one answer.

	A.
	B.
	C.
	D.
	E. All of the above

Question 37

Which of the following is a geometric series?

Choose one answer.

	A.
	B.
	C.
	D.
	E. All of the above

Question 38

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 39

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 40

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 41

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 42

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 43

If one put $1500 in an account where interest was compounded continuously, how many years would have to pass to raise the value of the account to $4500?

Choose one answer.

	A. 1 year
	B. 2 years
	C. 3 years
	D. 4 years
	E. It cannot be determined from the information given.

Question 44

Find the endpoints of the interval of convergence for the following power series:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 45

Find the endpoints of the interval of convergence for the following power series:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 46

Find the endpoints of the interval of convergence of the following power series:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 47

Solve

subject to the initial condition that the solution pass through (0, 1).

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 48

Solve

subject to the initial condition that the solution pass through (0, 2).

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 49

Calculate

Choose one answer.

	A. 1
	B.
	C. 2
	D.
	E. None of the above

Question 50

Calculate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 51

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 52

A bottle of water at 65 degrees Fahrenheit is put in a refrigerator at 35 degrees Fahrenheit. After an hour, the bottle has cooled to 50 degrees Fahrenheit. What will the temperature of the bottle be after another hour?

Choose one answer.

	A. 47.5 degrees Fahrenheit
	B. 45 degrees Fahrenheit
	C. 42.5 degrees
	D. 40 degrees Fahrenheit
	E. It cannot be determined from the information given.

Question 53

Find the Cartesian equation for the curve described by the parametric equations

and

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 54

Find the Cartesian equation for the curve described by the parametric equations

and

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 55

Find the equation of the tangent line to the curve described by

at the point corresponding to

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 56

Find the equation of the tangent line to the curve described by

at the point corresponding to

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 57

Consider the curve described by

. At the point corresponding to t = 1, which of the following best describes the curve?

Choose one answer.

	A. Concave up and increasing
	B. Concave down and increasing
	C. Concave up and decreasing
	D. Concave down and decreasing
	E. None of the above

Question 58

Consider the curve described by

. At the point corresponding to t = 1, which of the following best describes the curve?

Choose one answer.

	A. Concave up and increasing
	B. Concave down and increasing
	C. Concave up and decreasing
	D. Concave down and decreasing
	E. None of the above

Question 59

Compute

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 60

Compute

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 61

Compute

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 62

Find the area enclosed by the curve described by the polar equation

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 63

Find the length of the curve described by

for

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 64

Find the Cartesian equation for the curve described by the polar equation

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 65

Find the Cartesian equation for the curve described by the polar equation

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 66

Find the Cartesian coordinates of the point described by the polar coordinates:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 67

Find the Cartesian coordinates of the point described by the polar coordinates:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 68

Find the equation of the tangent line to the curve described by

, at the point corresponding to

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 69

Find the equation of the tangent line to the curve described by

, at the point corresponding to

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 70

Consider the curve described by

. At the point corresponding to

, which of the following best describes the curve?

Choose one answer.

	A. Concave up and increasing
	B. Concave down and increasing
	C. Concave up and decreasing
	D. Concave down and decreasing
	E. None of the above

Question 71

Consider the curve described by

. At the point corresponding to

, which of the following best describes the curve?

Choose one answer.

	A. Concave up and increasing
	B. Concave down and increasing
	C. Concave up and decreasing
	D. Concave down and decreasing
	E. None of the above

Question 72

Solve

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 73

Solve

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 74

Which of the following could be a formula for a sequence whose first four terms are 0.7, .91, .973, and .9919?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 75

What is the seventh term of the sequence given by

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 76

Find the limit of the sequence given by:

Choose one answer.

	A. 0
	B. 1
	C.
	D.
	E. None of the above

Question 77

Find the limit of the sequence given by

Choose one answer.

	A. 0
	B. 1
	C.
	D.
	E. None of the above

Question 78

Find the limit of the sequence given by

Choose one answer.

	A. 0
	B.
	C. 1
	D. 2
	E. None of the above

Question 79

Find the limit of the sequence given by

Choose one answer.

	A. 0
	B.
	C. 1
	D.
	E. None of the above

Question 80

What is the volume of the solid generated by rotating the region bounded by

, and

about the x-axis?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 81

What integral would you use to find the solid generated by rotating the region bounded by

and

around the line

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 82

What is the volume of the solid obtained by rotating the region bounded by

and

around the line

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 83

What integral would you use to find the solid generated by rotating the region bounded by

, and

around the line

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 84

What is the volume of the solid generated by rotating the region bounded by

and

around the y-axis?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 85

What integral could be used to calculate the volume of the solid generated by rotating the region bounded by

, and

around the line

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 86

What integral could you use to calculate the volume of the solid generated by rotating the region bounded by

about the line

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 87

What is the volume of the solid generated by rotating the positive region bounded by

and

around the x-axis?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 88

Calculate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 89

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 90

Calculate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 91

Find the indefinite integral:

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 92

What integral could you use to calculate the area of the surface of revolution generated by rotating the curve

around the x-axis?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 93

Find the Taylor series centered at

for the function

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 94

Find the Taylor series centered at

for

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 95

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 96

Calculate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 97

Calculate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 98

Evaluate $\int \frac{x^3}{\sqrt{x^2 +9}dx$ .

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 99

Evaluate

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above

Question 100

Evaluate

Choose one answer.

	A.
	B.
	C. 1
	D.
	E. None of the above

Question 101

Recalling that the force exerted by a spring as it is stretched is

, where

is the spring constant and

is the displacement from equilibrium, what integral would you use to find the work done in stretching a spring with constant

3 units from equilibrium?

Choose one answer.

	A.
	B.
	C.
	D.
	E. None of the above