Multivariable Calculus MA 241-02

Exam #1

Wednesday, Feb. 23, 8:00 am

The first exam covers Chapters 12 and 13. It is recommended that you go over the homework problems 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 12 and 13 Reviews and Check Your Understanding Sections below. Note that these problems are a SAMPLE selection. Certain topics are covered in the reviews better than others. The odd answers are in the back of the book while the evens are listed here. The exam will be designed to take the full class period (45-50 minutes).

Exam Review: We will review for the exam on Monday, Feb. 21, during class. Please come prepared with specific questions.

Chapter 12 Review, pp. 600 - 601
Problems:   2, 5, 7, 9, 14, 15, 17, 18, 19, 21, 24, 25, 30, 31, 32

The answers to the evens are:
2.   x/5 + y/3 + z/2 = 1
14.   (a) goes with (ii), (b) goes with (i)
18.   Not True
24.   (a) level curves are concentric circles, NOT equally spaced, (b) z = cos x, (c) z = cos r, where r^2 = x^2 + y^2
32.   f(0,t) gives the displacement of the left-end of the string over time while f(1,t) gives the displacement of the point (bug) at x = 1 over time

Chapter 12 Check Your Understanding, pp. 602 - 603
Problems:   11, 13, 17, 31, 33, 35, 39, 51, 55

Chapter 13 Review, pp. 635 - 636
Problems:   3, 5, 7, 8, 9, 10, 11, 13, 15, 17, 18, 19, 20, 26, 27, 28

The answers to the evens are:
8.   0
10.   10/sqrt(14) (2i + 3j - k)
18.   sqrt(6)/2
20.   0.4 v i + 0.7 v j
26.   (a) 53.1 degrees east of south, (b) Not gonna make it!
28.   2/sqrt(21)

Chapter 13 Check Your Understanding, pp. 637
Problems:   3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 26

The answers to the evens are:
4.   False     26.   True