Calculus for the Social Sciences II (Sections 01 and 02)

Exam #3

Thursday, April 24, In Class

The second exam covers Sections 6.4 through 7.4, excluding Section 6.5. Note however, that much of the material from previous sections is still quite relevant (eg. Integration formulas, FTC part II, u-sub, etc..) It is recommended that you go over homework problems (HW#7 - 9), past quizzes 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 6 and 7 Review Exercises below. Note that certain sections are not well-covered in the Chapter Review Exercises (such as the Econ examples from Section 6.6 and intro ODE's in Section 7.1). 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: We will review for the exam in class on Tuesday, April 22. 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 6 Review Exercises, pp. 494 - 495
Problems:   25, 26, 29, 31

Note: For problem #31, since the mean is 8, the constant k in the exponential density function is 1/8 (the reciprocal of the mean.)
The answer to the even problem is:
26.   26/9

Chapter 7 Review Exercises, pp. 551 - 553
Problems:   1, 3, 4, 6, 7, 8, 16

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!)
16.   (a) 140/3 = 46.666666 degrees Celsius, (b) about 1 hour, 21 minutes