AP Calculus MATH 136-01

Exam #3

Wednesday, Dec. 1 IN CLASS

The third exam covers Chapters 8, 9 and 10. Specifically, this is sections 8.1, 8.2, 8.3, 9.1, 9.2, 9.3, 9.4, 10.1, 10.2, and 10.3. It is recommended that you read over the Chapter Topic Review Sheets to make sure you understand the vocabulary and concepts from all three chapters.

An excellent way to study is to go over the homework problems as well as your class notes. Many of the problems and questions we discussed in class are excellent examples of test questions. I have also listed some sample problems from the Chapter Reviews and "Check Your Understanding" problems below. The odd answers are in the back of the book while the evens are listed here. The exam will be designed to take the full class period (45-50 minutes).

Exam Review: We will review for the exam on Monday, Nov. 29th, during class. Please come prepared with specific questions.

Note: You will be given a scientific calculator for the exam which does NOT have graphing capabilities so be prepared to answer questions without your personal calculator.

Chapter 8 review, pp. 397-401
Problems:   3, 5, 9, 10, 11, 13, 15, 16, 17

The answers to the evens are:
10a.   5Pi/6
10b.   4Pi/5
16.   1/4

Chapter 8 "Check Your Understanding", pp. 401
Problems:   1, 5, 8, 9, 10, 12

All of the evens above are FALSE.

Chapter 9 review, pp. 429-430
Problems:   1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16

The answers to the evens are:
2.   Use the fact that |sin(n)| <= 1.
8.   Converges by the ratio test.
10.   Converges by the alternating series test.

Chapter 9 "Check Your Understanding", pp. 431
Problems:   6, 7, 11, 22, 23, 24

6.   FALSE
7.   TRUE
11.   FALSE
22.   TRUE
23.   FALSE
24.   FALSE

Chapter 10 review, pp. 470 -473
Problems:   1, 3, 6, 7, 8, 9, 12, 13, 15, 17, 19, 20, 23

The answers to the evens and #1 are:
1.   e + e(x-1) + e(x-1)^2/2
6.   th^2 - th^6/2! + th^10/4! - th^14/6! + - ... (th = theta)
8.   1/2 + x/16 + 3x^2/256 + 5x^3/2048 + ...
12.   (a) 7(1.02^104 - 1)/(0.02*1.02^100)     (b) 7e^(0.01)
20.   1- cos(x) < x sqrt(1-x) < ln(1+x) < arctan(x) < sin(x) < x < e^x - 1

Chapter 10 "Check Your Understanding", pp. 473-474
Problems:   1, 3, 8, 9, 13