Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.1 - Functions of Several Variables - Exercises 14.1 - Page 787: 11

Answer

$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $(x-2)(x+2)(y-3)(y+3)\geq 0$ $\}$
1578463769

Work Step by Step

$f$ is defined when the radicand is nonnegative, $(x^{2}-2^{2})(y^{2}-3^{2})(y+3)\geq 0$ $(x-2)(x+2)(y-3)(y+3)\geq 0$ To graph, we draw (solid) lines$ \left\{\begin{array}{l} x=2\\ x=-2\\ y=3\\ y=-3 \end{array}\right.$, These four lines split the plane in 9 regions. Taking a test point from each region, we find that $(-4,4), (4,4), (0,0), (-4,-4)$ and $(4,-4)$ satisfy the inequality, and the others do not. Shade regions containing the testpoints that satisfy the inequality. Domain: $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $(x-2)(x+2)(y-3)(y+3)\geq 0$ $\}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.