AP Calculus MATH 136-04

Exam #2

Wednesday, Nov. 1, IN CLASS

The second exam covers Chapter 3, Chapter 4 (excluding Sections 4.4, 4.7 and 4.8), and Sections 5.1 - 5.6. It is recommended that you go over the homework problems (HW#4 - 7) 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 3, 4 and 5 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, Oct. 30th, 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 3 Review Exercises, pp. 255 - 257
Problems:   2, 3, 7, 10, 13, 20, 21, 23, 25, 27, 28, 33, 37, 39, 47, 61, 64 (a,b,c,e), 71a, 73

The answers to the evens are:
2.   -sin(tan x) sec^2(x)
10.   e^x/sqrt(1-e^(2x))
20.   Use logarithmic differentiation.
28.   -sin(x) e^(cos x) - e^x sin(e^x)
64.   (a) v = 3t^2 - 12, a = 6t, (b) upward: t > 2, downward: 0 < t < 2, (c) 23, (e) speeding up: t > 2, slowing down: 0 < t < 2.

Chapter 4 Review Exercises, pp. 336 - 338
Problems:   1, 3, 5, 7, 8, 23, 25, 27, 29, 31, 34, 35, 37, 38, 43, 45, 51, 53

The answers to the evens are:
8.   (a) vertical asymptotes at x = 1,-1 and horiz. asymp. at y = 0, (b) decreasing: (-infty, -1) and (-1,0), increasing: (0,1) and (1,infty), (c) local min at the point (0,1), (d) concave up: (-1,1) and concave down: (-infty,-1), (1,infty).
34.   8/(9 Pi) cm/s.
38.   The point is (4,2).

Chapter 5 Review Exercises, pp. 434 - 436
Problems:   1, 3, 5, 7, 8, 9, 13, 15, 19, 21, 24, 25, 27, 32, 33, 34, 39, 41, 65

The answers to the evens are:
8.   (a) e^(Pi/4) - 1, (b) 0, (c) e^(arctan x)
24.   (25 - 100 e^(-3))/9
32.   x arctan(x) - ln(1+x^2)/2 + c
34.   0