Multivariable Calculus

Homework Assignment #3

Due Friday, September 21, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to McCallum's book, the required text for the course. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work.

Section 11.6
Problems:   3, 4, 5, 9, 13-19 all

Hint: For #5, use the t-values t = 0, t = Pi/3, and t = Pi. For each one of these values, draw a contour diagram in the xy-plane. Choose a few function values and sketch the level curves in the xy-plane. Your answer should consist of three separate contour plots. For #13-19 use the catalog of surfaces on page 48. State which surface the equation represents and say a little bit about the surface (eg. hyperboloid of two sheets centered about the x-axis).

Section 11.7
Problems:   1, 2, 5, 8, 9, 11, 12, 15, 16

Hint: For #15 and #16, try picking a few key points in the domain. If the c-value needed to make the function continuous changes from one point to another, there is no one c-value which makes the function continuous everywhere.

Section 12.1
Problems:   1, 3, 6, 8, 14, 23, 24, 26, 28, 30, 32