Calculus for Social Sciences II (Section 03)

Exam #3

Thursday, April 29, In Class

The third exam covers Sections 6.2, 6.5, 6.7, 6.8 and 7.1 through 7.4. Note however, that as with Exam #2, 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), quizzes #7 - 9, and 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. In addition, you can now use WebAssign to practice exercises similar to homework problems by clicking on the "practice another version" tab at the bottom of each problem.

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 6.7 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 27. 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. 488 - 490
Problems:   6, 9, 10, 12, 33, 34, 37, 39

Note: For problem #39, 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 problems are:
6.   pi(25/12 + 1/(4 e^4) )
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