The third exam covers Sections 7.7 - 7.9, 8.1, and Chapter 10. However, some material from the previous exams (e.g., u-substitution, integration formulas) is still important to review. It is recommended that you go over homework problems (HW #7 - 9, both written and WebAssign), 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, Nov. 27th. 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, 22, 28, 29, 32, 33, 37, 38, 39, 42, 43, 47, 48, 56, 57, 65, 68, 69, 77, 79, 83, 84, 85, 87, 88, 90, 91, 93, 100, 101, 102, 103, 104, 113, 127

The answers to the evens are:
10.   -3/2
14.   0
22.   2/3
28.   4/5
32.   4/(e² - 2e)
38.   π/12; the total area is the sum of a geometric series with ratio r = 1/4.
42.   converges; integral = 1/(4e).
48.   converges; use the Limit Comparison Test with 1/3ⁿ.
56.   converges conditionally; the original series converges by the Alternating Series Test, but the series of absolute values diverges using the Limit Comparison Test with the Harmonic Series.
68.   converges by the ratio test (limit is 0).
84.   converges by the ratio test (limit is 0).
88.   diverges by the nth term divergence 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).