Answer
$\lim\limits_{x \to 2}\frac{x}{x²-4}$ does not exist.
Work Step by Step
$\lim\limits_{x \to 2^{+}}\frac{x}{x²-4}$ = +$\infty$. See exercise 18.
$\lim\limits_{x \to 2^{-}}\frac{x}{x²-4}$ = -$\infty$. See exercise 19.
As $\lim\limits_{x \to 2^{+}}\frac{x}{x²-4}$ $\ne$ $\lim\limits_{x \to 2^{-}}\frac{x}{x²-4}$, we conclude that $\lim\limits_{x \to 2}\frac{x}{x²-4}$ does not exist.
