Answer
$$
\lim _{x \rightarrow 3^{-}} e^{2 /(x-3)}=0
$$
Work Step by Step
$$
\lim _{x \rightarrow 3^{-}} e^{2 /(x-3)}
$$
Let
$$
t=2 /(x-3) . \text { As } x \rightarrow 3^{-}, t \rightarrow-\infty .
$$
So,
$$
\lim _{x \rightarrow 3^{-}} e^{2 /(x-3)}=\lim _{t \rightarrow-\infty} e^{t}=0
$$
