Question

Solve $\underset{x\to 0}{lim}\frac{\cos x}{\pi -x}$

Answer 1

We have,

${lim}_{x\to 0}\left(\frac{\cos x}{\pi -x}\right)$

Apply L-Hospital rule,

$\Rightarrow {lim}_{x\to 0}\left(\frac{-\sin x}{0-1}\right)$

$\Rightarrow {lim}_{x\to 0}\left(\sin x\right)$

$\Rightarrow \sin 0$

$\Rightarrow 0$

Hence, this is the answer.