Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise - Page 911: 32

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

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