Question

Solve :
$\underset{x\to 0}{lim}\frac{\sin \left(\pi {\cos }^{2}x\right)}{x^2}$

Answer 1

$\begin{array}{c}{lim}_{x\to 0}\frac{\sin \left(\pi {\cos }^{2}x\right)}{x^2}\\ {lim}_{x\to 0}\left(\frac{\cos \left(\pi {\cos }^{2}x\right).\pi .2\cos x\left(-\sin x\right)}{2x}\right)\\ {lim}_{x\to 0}\pi \cos \left(\pi {\cos }^{2}x\right).\cos x\left(\frac{-\sin x}{x}\right)\\ \pi \left(-1\right)\left(-1\right)\\ =\pi \end{array}$