Answer
$\infty$
Work Step by Step
Need to find the limit for $\lim\limits_{x \to2^{-}}e^{\frac{3}{(2-x)}}$.
Consider $y=\lim\limits_{x \to2^{-}}e^{\frac{3}{(2-x)}}$
when ${x \to 2^{-}}$ then $(2-x) \to 0^{+}$
Thus, $\lim\limits_{x \to2^{-}}e^{\frac{3}{(2-x)}}=e^{\infty}$
Hence, the limit for $\lim\limits_{x \to2^{-}}e^{\frac{3}{(2-x)}} $ is $\infty$.