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: 8

Answer

$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x^{2}+y^{2}\neq 25$ $\}$
1578461762

Work Step by Step

There are no restricitions on sine, since it is is defined everywhere. f is defined for points (x,y) that do not yield zero in the denominator. We exclude all points for which $x^{2}+y^{2}=25$ This is a circle about the origin of radius $5$. Since we are excluding it, we graph it with a dashed line. Domain: all points not lying on circle $x^{2}+y^{2}=25$ or, in set notation, $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x^{2}+y^{2}\neq 25$ $\}$
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