The third exam covers Sections 7.7 - 7.9, 8.1, and 10.1 - 10.6. However, some material from the previous exam (e.g., u-substitution, integration formulas) should be reviewed for this exam as well. It is recommended that you go over homework problems (HW #7 - 9, both written and WebAssign), Computer Project #2, class notes, and worksheets. Many of the problems and questions we discuss in class are excellent examples of test questions. The solutions to your WebAssign problems on HW #7 - 9 can be seen by clicking "View Key" near the top of each assignment. You can also click on "Practice Another Version" to redo certain homework problems.

In addition, some review problems from the Chapter 7, 8, and 10 Review Exercises are listed below. The odd answers are in the back of the book while the evens are listed here. The exam will be designed to take roughly one hour although you will have 90 minutes if needed.

We will review for the exam during class on Tuesday, April 23. Please come prepared with specific questions.

Note: You will be allowed a scientific calculator for the exam which does NOT have graphing or symbolic capabilities. Please bring your own calculator with you to the exam.

Chapter 7 Review Exercises, pp. 440 - 442
Problems:   69, 70, 72, 75, 76, 77, 79, 82, 83, 84, 99, 100, 103, 104

The answers to the evens are:
70.   Show that the integral from 0 to ∞ equals 1. The mean is 5/2.
72.   To find the average, compute the mean = 8. The probability is the integral of the PDF from 0 to 3, which gives 1 - e^-0.375 ≈ 0.31271.
76.   The integral diverges.
82.   ln 2 - ln(5/3) or ln(6/5).
84.   3^5/3/2.
100.   T₃ = 25.976514.
104.   S₈ = 0.608711.

Chapter 8 Review Exercises, pp. 476 - 477
Problems:   1, 2, 3

The answer to the even problem is:
2.   e - e^-1.

Chapter 10 Review Exercises, pp. 575 - 577
Problems:   10, 11, 13, 14, 15, 28, 29, 32, 33, 37, 39, 42, 43, 47, 57, 58, 65, 68, 69, 77, 79, 83, 84, 85, 87, 88, 90, 91, 100, 101, 102, 103, 104

The answers to the evens are:
10.   -3/2
14.   0
28.   4/5
32.   4/(e² - 2e)
42.   converges; integral = 1/(4e).
58.   converges conditionally; write out the first few terms to see the pattern. The original series converges by the Alternating Series Test, but the series of absolute values diverges by the p-series test.
68.   converges by the ratio test (limit is 0).
84.   converges by the ratio test (limit is 0).
88.   diverges by the nth term test.
90.   converges by the ratio test (limit is 0).
100.   converges by the ratio test (limit is 0).
102.   -1 ≤ x < 1 or [-1,1).
104.   -1 < x < 1 or (-1,1).