Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.1 Functions of Two or More Variables - Exercises - Page 763: 10

Answer

The domain $D$ consists of all points $\left( {x,y} \right)$ with $x=0$ excluded: $D = \left\{ {\left( {x,y} \right)|x \ne 0} \right\}$

Work Step by Step

The function $f\left( {x,y} \right) = \sin \frac{y}{x}$ is defined only when $x \ne 0$. Thus, the domain $D$ consists of all points $\left( {x,y} \right)$ with $x=0$ excluded: $D = \left\{ {\left( {x,y} \right)|x \ne 0} \right\}$
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