Answer
$\lim\limits_{x \to 3}\frac{x}{x-3}$ does not exist.
Work Step by Step
$\lim\limits_{x \to 3^{+}}\frac{x}{x-3}$ = $+\infty$. See exercise 15.
$\lim\limits_{x \to 3^{-}}\frac{x}{x-3}$ = $-\infty$. See exercise 16.
As $\lim\limits_{x \to 3^{+}}\frac{x}{x-3}$ $\ne$ $\lim\limits_{x \to 3^{-}}\frac{x}{x-3}$, we conclude that $\lim\limits_{x \to 3}\frac{x}{x-3}$ does not exist.
