AP Calculus MATH 136-04

Exam #3

Wednesday, Nov. 29, IN CLASS

The third exam covers Sections 5.7, 5.10, 6.1, 6.2 and Chapter 8 (excluding sections 8.8, 8.9). It is recommended that you go over the homework problems (HW#8 - 10) as well as your class notes. Many of the problems and questions we discuss in class are excellent examples of test questions. I have also listed some sample problems from the Chapter 5, 6 and 8 Review Exercises below. The odd answers are in the back of the book while the evens are listed here. Note that some sections are poorly covered by the problems in the Chapter Reveiw Exercises (eg. trig. substitution is missing in Ch. 5.) 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. 27th, 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. 434 - 436
Problems:   29, 55, 57, 58, 59

The answers to the evens are:
58.   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. 494 - 495
Problems:   1, 2, 4, 6a, 6b, 7

The answers to the evens are:
2.   32/3 (Horizontal cross-sections, integrate with respect to y.)
4.   Pi(25/12 + e^(-4)/4) (Washer method)
6.   (a) 5/12, (b) 41Pi/105 (Washer method)

Chapter 8 Review Exercises, pp. 632 - 633
Problems:   1, 5, 9, 10, 11, 13, 15, 19, 21, 22, 31, 32, 33, 35, 37, 39, 40, 41, 49

The answers to the evens are:
10.   diverges (Compare to harmonic series)
22.   e^(-e) (This is the Taylor series for e^x evaluated at x = -e.)
32.   Converges for all real numbers, radius of convergence = infinity.
40.   x + 2x^2 + 2x^3 + 4x^4/3 + 2x^5/3 + ... + 2^n x^(n+1)/n! + ...