Evaluate the given limit: $\mathop {\lim }\limits_{x \to \pi } \frac{\sin (\pi-x)}{\pi(\pi-x)}$

$\lim _{x \rightarrow 0} \frac{\sin ^{2}\left(\pi \cos ^{4} x\right)}{x^{4}}$ is equal to :

$\mathop {\lim }\limits_{h \to 0} \frac{{2\left[ {\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)} \right]}}{{\sqrt 3 h(\sqrt 3 \cos h - \sin h)}} = $

$\mathop {\lim }\limits_{x \to 0} \frac{\sin 2x}{x} = $

$\lim _{x \rightarrow 0} \frac{\tan ^4 x-\sin ^4 x}{x^6} = $

Evaluate the limit: $\lim_{x \rightarrow \infty} x \sin \left(\frac{2}{x}\right)$