## Thomas' Calculus 13th Edition

$1$
Here, $\lim\limits_{(x,y) \to (0,0)} e^y(\dfrac{\sin x}{x})=e^{0} \lim\limits_{(x \to0)} (\dfrac{\sin x}{x})$ Then, we have $\lim\limits_{(x,y) \to (0,0)} e^y(\dfrac{\sin x}{x})=(1)(1)=1$