$\lim _{x \rightarrow 0} \left( \frac{\tan x}{\sqrt{2x+4}-2} \right)$ is equal to

If $f(x)$ satisfies $97 f(x) + m f\left(\frac{1}{x}\right) = 0$,where $f(x) = \lim_{n \rightarrow \infty} n(x^{1/n} - 1)$ for $x > 0$,then the value of $m$ is:

For the function $f(x) = (1 + \frac{1}{x})^x$,which of the following limits tends to unity?

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:

The value of the limit $\lim _{x \rightarrow-\infty}\left(\sqrt{4 x^2-x}+2 x\right)$ is

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 3} \frac{x^{4}-81}{2 x^{2}-5 x-3}$