$\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{3 x}=$

$\lim _{x \rightarrow 0} \frac{|x|}{|x|+x^2} = $

Evaluate the limit: $\mathop {\lim }\limits_{x \to 3} (x+3)$

If $\lim _{x \rightarrow 0} \frac{\left(e^{k x}-1\right) \sin k x}{x^{2}}=4$,then $k$ is equal to

The value of $\lim_{h \rightarrow 0} 2 \left\{ \frac{\sqrt{3} \sin (\frac{\pi}{6} + h) - \cos (\frac{\pi}{6} + h)}{\sqrt{3} h (\sqrt{3} \cos h - \sin h)} \right\}$ is

The value of $\lim_{x \to 0} (\frac{8}{x^8}) [1 - \cos \frac{x^2}{2} - \cos \frac{x^2}{4} + \cos \frac{x^2}{2} \cdot \cos \frac{x^2}{4}]$ is equal to: