Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises - Page 951: 32


$D=$ {$(x,y) | x \neq 0,y \neq 0$}

Work Step by Step

As we are given that $h(x,y)=\dfrac{e^x+e^y}{e^{xy}-1}$ The function $h(x,y)=\dfrac{e^x+e^y}{e^{xy}-1}$ represents a rational function which is continuous on its domain $D$. Thus, $ e^{xy}-1 \neq 0$ or, $e^{xy} \neq 1$ This means that $x \neq 0,y \neq 0$ Hence, Domain: $D=$ {$(x,y) | x \neq 0,y \neq 0$}
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