Let for all $x > 0$,$f(x) = \lim_{n \rightarrow \infty} n(x^{1/n} - 1)$,then

$\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

$\lim _{x \rightarrow 0} \frac{\sqrt{\cos x} - \sqrt[3]{\cos x}}{\sin ^2 x} = $

For each $t \in R$,let $[t]$ be the greatest integer less than or equal to $t$. Then $\lim_{x \to 0^+} x \left( [\frac{1}{x}] + [\frac{2}{x}] + \dots + [\frac{15}{x}] \right) = $

The value of $\mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos (1 - \cos x)}}{{x\tan x - {x^2}}}$ is:

Find $\mathop {\lim }\limits_{x \to 5} f(x),$ where $f(x)=|x|-5$.