Multivariable Calculus, MATH 241

Exam #3

Wednesday, April 22, In Class

The second exam covers Sections 9.7, 11.7, 11.8, 12.1 - 12.4, 12.7 and 12.8. It is recommended that you go over homework problems (HW #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, some review problems from the Chapter 9, 11, and 12 Review Exercises are listed below. The odd answers are in the back of the book while the evens are listed here. The Concept Check problems at the end of each chapter (before the Exercises) are also a good source of questions. The exam will be designed to take the full class period (45-50 minutes).

Note: You will be allowed a scientific calculator for the exam which does NOT have graphing capabilities. Please bring your own calculator.

Exam Review: We will review for the exam during Monday's class on April 20. Please come prepared with specific questions.

Chapter 9 Review, p. 689-690
Problems:   39, 40, 41, 42

The answers to the evens are:
40.   (a) The half-plane y = x, with x ≥ 0. (b) A cone facing upwards with equation z = sqrt{x2 + y2}.
42.   Cylindrical coordinates: r = 2. Spherical coordinates: ρ sin φ = 2.

Chapter 11 Review, p. 823-826
Problems:   51, 52, 53, 55, 59, 60, 61, 64

The answers to the evens are:
52.   (0,0) is a saddle point; (1,1/2) is a local minimum
60.   The absolute maximum is sqrt{2} and it occurs at (sqrt{2}, sqrt{2}); the absolute minimum is -sqrt{2} and it occurs at (-sqrt{2}, -sqrt{2}).
64.   Length 36, width and height both 18.

Chapter 12 Review, p. 900-902
Problems:   1, 3, 5, 7, 9, 10, 13, 15, 17, 19, 21, 22, 23, 28, 29, 30, 32, 34, 41

The answers to the evens are:
10.   y - 4 ≤ x ≤ 4 - y, 0 ≤ y ≤ 4
22.   (1/3)(23/2 - 1)
28.   π/14
30.   53/20
32.   12π
34.   π/6