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

Let $[x]$ denote the greatest integer less than or equal to $x$. Then,evaluate the limit: $\mathop {\lim }\limits_{x \to 0} \,\frac{{\tan \,(\pi \,{{\sin }^2}\,x) + \,{{(\left| x \right|\, - \,\sin \,(x\,[x]))}^2}}}{{{x^2}}}$

If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^{2} x}}$,then $\lim_{x \rightarrow \infty} f(x)$ is

If $\lim_{x}$ ${\rightarrow 0} \left\{ \frac{1}{x^{8}} \left( 1 - \cos \frac{x^{2}}{2} - \cos \frac{x^{2}}{4} + \cos \frac{x^{2}}{2} \cos \frac{x^{2}}{4} \right) \right\} = 2^{-k}$,then the value of $k$ is

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

If $0 \leq x \leq \pi / 2$,then $\lim _{x \rightarrow a} \frac{|2 \cos x-1|}{2 \cos x-1}$