Calculus for Social Sciences 1 (Sections 01 and 02)

Exam #3

Tuesday, Nov. 27, In Class

The second exam covers all of Chapter 3 (excluding Section 3.8) and Sections 4.2 and 4.3. It is recommended that you go over homework problems (HW#7 - 9) 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 and 4 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 roughly one hour although you will have the full class period (plus a little extra) if necessary.

Exam Review Session: Monday, Nov. 26, 7:00 - 8:30 pm in O'Neil 112.

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:   1, 2, 3, 4, 7, 9, 10, 11, 13, 15, 16, 21, 23, 25, 27, 28, 33, 35, 37, 39, 47, 48, 61, 64 (a,b,c,e), 69

The answers to the evens are:
2.   -sin(tan x) sec^2(x)
4.   (3x + 5)/(2x + 1)^(3/2)
10.   e^x/sqrt(1-e^(2x))
16.   (y - 2x cos y)/(2 cos(2y) - x^2 sin y - x)
28.   -sin(x) e^(cos x) - e^x sin(e^x)
48.   (a) -2, (b) -3/8, (c) 6
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, 2, 3, 5, 6, 7, 8

The answers to the evens are:
2.   f(1/4) = -1/4 is a local min and absolute min, f(4) = 2 is the absolute max.
6.   (a) no asymptotes, (b) increasing on (-3,0), (0, infinity), decreasing on (-infinity, -3), (c) local min at f(-3) = -27, no local max, (d) concave up on (-infinity, -2), (0, infinity), concave down on (-2, 0), inflection points at (-2,-16) and (0,0)
8.   (a) vertical asymptotes at x = 1,-1 and horiz. asymp. at y = 0, (b) decreasing on (-infinity, -1) and (-1, 0), increasing on (0, 1) and (1, infinity), (c) local min at the point (0,1), (d) concave up on (-1, 1) and concave down on (-infinity, -1), (1, infinity), no inflection points.