Figure

$\lim\limits_{(x,y) \rightarrow (0,0)}e^{x^{2}+y^{2}}\underset{\underset{\color{#0066A7}{\hbox{Example 6(a)}}}{\color{#0066A7}{\uparrow}}}{=}e^{0+0}=1$
$\lim\limits_{(x,y) \rightarrow ( \sqrt{\pi },0) }\sin e^{x^{2}+y^{2}}\underset{\underset{\color{#0066A7}{\hbox{Example 6(b)}}}{\color{#0066A7}{\uparrow}}}{=}\sin e^{\pi }$
$\lim\limits_{(x,y) \rightarrow (e,1) }\ln \dfrac{y}{x}\underset{\underset{\color{#0066A7}{\hbox{Example 6(c)}}}{\color{#0066A7}{\uparrow}}}{=}\ln \dfrac{1}{e}=\ln e^{-1}=-1$