1
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 to .
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
If 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
.
.