|
|
$\mathop {\lim }\limits_{x \to 0}\frac{\cos (\frac{\pi}{2}\cos x)}{\sin^2(\frac{x}{2})}=\mathop {\lim }\limits_{x \to 0}\frac{\sin (\frac{\pi}{2}-\frac{\pi}{2}\cos x)}{\sin^2(\frac{x}{2})}=\mathop {\lim }\limits_{x \to 0}\frac{\sin \left ( \pi\sin^2(\frac{x}{2}) \right )}{\sin^2(\frac{x}{2})}=\mathop {\lim }\limits_{x \to 0}\frac{\sin \left ( \pi\sin^2(\frac{x}{2}) \right )}{\pi\sin^2(\frac{x}{2})}.\pi=1.\pi=\pi$
|