Questions in fun-lim

Select	Question
	$\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi {{\cos }^{2}}x)}{{{x}^{2}}}=$
	$\underset{x\to 3}{\mathop{\lim }}\,\,[x]=$ , (where [.] = greatest integer function)
	If $f(x) =\begin{vmatrix} {\sin x}&{\cos x}&{\tan x}\\ {{x^3}}&{{x^2}}&x\\ {2x}&1&1 \end{vmatrix}$, then $\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{{{x}^{2}}}$ is
	$\lim\limits_{x\to0}\frac{\log_e(1+x)}{3^x-1}$
	$\underset{x\to 0}{\mathop{\lim }}\,\,\,\cos \frac{1}{x}$
	Let $f(x)=4$ and $f'(x)=4$ , then $\underset{x\to 2}{\mathop{\lim }}\,\,\frac{xf(2)-2f(x)}{x-2}$ equals
	$\underset{x\to \infty }{\mathop{\lim }}\,\frac{\log {{x}^{n}}-[x]}{[x]},\,n\in N,\,$ $\,(\,[x]$ denotes greatest integer less than or equal to x)
	If $f(1)\,=1,\,{f}'\,(1)\,=2$ , then $\underset{x\to 1}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-1}{\sqrt{x}-1}$ is
	$\underset{n\to \infty }{\mathop{\lim }}\,\,{{\left( \frac{{{n}^{2}}-n+1}{{{n}^{2}}-n-1} \right)}^{n(n-1)}}=$
	$\underset{x\to 0}{\mathop{\lim }}\,\frac{{{4}^{x}}-{{9}^{x}}}{x({{4}^{x}}+{{9}^{x}})}=$