Multivariable Calculus

Prof. Gareth Roberts

Homework Assignment #5

Due Wednesday, March 11, start of class

There are two parts to this assignment, an online component using the program WebAssign, and a hand-written portion that should be turned at the START of class.

The instructions on WebAssign may be different than those in the textbook. (You can ignore these differences.) It is recommended that you keep any hand-written work used to complete these problems so that you can learn from it later on and have something to refer to should you require extra help. It is expected that when you login to WebAssign to complete your homework, you will be working on your own.

Note: Some of the problems on WebAssign are randomized so that they will have different numbers (shown in red) than those in the book. This helps insure students are doing their own work and is a nice way to practice the same type of problem before an exam.

The problems to be turned in by hand are indicated below. All problem numbers refer to Multivariable Calculus, Concepts and Contexts 4th ed., by Stewart. Unless stated otherwise, you should do all parts of a problem (e.g., (a), (b), (c), etc.). You should write up your solutions neatly, making sure to SHOW ALL YOUR WORK. Be sure to read the directions to each problem carefully. You are encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

Important: At the top of your written homework, please list the names of any students or faculty who you worked with on the assignment.

Section 11.2, pp. 755 - 756
Problems: 8, 15, 30, 33

Hints: For #8, try taking the limit along the x-axis and then again along the y-axis. Compare your results. For #15, multiply top and bottom by the conjugate and simplify. Then take the limit.

Section 11.3, pp. 766 - 769
Problems: 10, 57, 68

Hints: For #10, to estimate a given partial derivative, take the average of two slopes. For instance, to estimate fx(2,1), use the contour plot to find the change in f moving to the right starting at (2,1) and also moving to the right but ending at (2,1). Then average the two slopes. For #68, interpret fxy as measuring the change in fy in the x direction (i.e., as you walk from P in the positive x-direction, does fy increase or decrease in value?)