## Calculus 8th Edition

Published by Cengage

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

#### Answer

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

#### 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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