AP Calculus MATH 136-04

Exam #3

Wednesday, Dec. 1, IN CLASS

The third exam covers Sections 5.8 - 5.10, 6.1, 6.2, 6.4, 6.5, 6.8 and 7.1 - 7.4. It is recommended that you go over the homework problems (HW#7 - 9) and quizzes (#7 and 8), as well as your class notes. 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 click ``Practice Another Version'' after each problem to try the same problem but with different numbers.

I have also listed some sample problems from the Chapter 5, 6 and 7 Review Exercises below. The odd answers are in the back of the book while the evens are listed here. The Concept-Check at the end of each chapter (before the exercises) is also a source for good questions. 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 5 Review Exercises, pp. 425 - 427
Problems:   43, 44, 46, 47, 50, 55, 57, 58, 59

The answers to the evens are:
44.   (-1/4)cot(t) csc^3(t) - (3/8)csc(t) cot(t) + (3/8)ln|csc(t) - cot(t)| + c
46.   ln|(sqrt[1+2sin(x)] - 1)/(sqrt[1+2sin(x)] + 1)| + c
50.   17.736016
58.   Diverges. Break the integral into two integrals, from 0 to 2/3 and from 2/3 to 1. The first of these diverges so the original integral diverges.

Chapter 6 Review Exercises, pp. 488 - 490
Problems:   1, 3, 4, 6, 9, 10, 11, 12, 23, 25, 34, 37, 39

The answers to the evens are:
4.   32/3 (Horizontal cross-sections, integrate with respect to y.)
6.   Pi(25/12 + e^(-4)/4) (Washer method)
10.   117 pi/5
12.   256 pi
34.   26/9

Chapter 7 Review Exercises, pp. 548 - 550
Problems:   1, 3, 4, 6, 7, 8, 14

The answers to the evens are:
4.   (a) y(0.4) = 1.08, (b) y(0.4) = 1.129238, (c) y = 1/(1-x^2), y(0.4) = 25/21 = 1.190476 so decreasing the step-size leads to a better approximation although it is still considerably off.
6.   x = c e^(t - t^2/2) - 1
8.   y = ln( (3 - cos x)/(1 + cos x) ) (Hard one!)
14.   (a) 140/3 = 46.666666 degrees Celsius, (b) about 1 hour, 21 minutes