Answer
$\lim\limits_{x \to 4}\frac{3-x}{x²-2x-8}$ does not exist.
Work Step by Step
As $\lim\limits_{x \to 4^{-}}\frac{3-x}{x²-2x-8}$ = +$\infty$ $\ne$ $\lim\limits_{x \to 4^{+}}\frac{3-x}{x²-2x-8}$ = -$\infty$, we conclude that $\lim\limits_{x \to 4}\frac{3-x}{x²-2x-8}$ does not exist.
