Answer
$0$
Work Step by Step
Consider $f(x)=\lim\limits_{x \to \pi}\dfrac{\tan x}{x}=\lim\limits_{x \to 1} \dfrac{a(x)}{b(x)}$ and $a(\pi)=\pi, b(\pi)=0$
Thus, $f(\pi)=\dfrac{\pi}{0}$
This shows an Inderminate form of the limit, so apply L-Hospital's rule:
$\lim\limits_{x \to l}\dfrac{a(x)}{b(x)}=\lim\limits_{x \to l}\dfrac{a'(x)}{b'(x)}$
Thus,
$\lim\limits_{x \to \pi}\dfrac{\tan \pi}{\pi}=0$
