$\mathop {\lim }\limits_{x \to 0} \frac{{3\sin x - \sin 3x}}{{{x^3}}} = $

$\mathop {\lim }\limits_{x \to 0} \frac{{{a^{\sin x}} - 1}}{{{b^{\sin x}} - 1}} = $

$\lim _{x \rightarrow 0^{-}} \frac{\sqrt{\frac{1}{2}(1-\cos ^2 x)}}{x}$ is equal to

$\lim _{t}$ ${\rightarrow 0}\left(1^{\frac{1}{\sin ^2 t}}+2^{\frac{1}{\sin ^2 t}}+\ldots +n^{\frac{1}{\sin ^2 t}}\right)^{\sin ^2 t}$ is equal to $.......$

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

$\lim _{x \rightarrow \pi} \frac{1-\sin (x/2)}{\left(\cos \frac{x}{2}\right)\left(\cos \frac{x}{4}-\sin \frac{x}{4}\right)} =$