Questions in fun-lim

Select	Question
	$\underset{x\to 0}{\mathop{\lim }}\,{{\left( \frac{1+\tan x}{1+\sin x} \right)}^{\text{cosec }x}}$ is equal to
	$\underset{n\to \infty }{\mathop{\lim }}\,{{({{4}^{n}}+{{5}^{n}})}^{1/n}}$ is equal to
	The value of $\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{2}}\sin \frac{1}{x}-x}{1-\|x\|}$ is
	$\underset{x\to \infty }{\mathop{\lim }}\,\sqrt{\frac{x+\sin x}{x-\cos x}}=$
	$\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}=$
	If $0
	The value of $\underset{x\to \infty }{\mathop{\lim }}\,\sqrt{{{a}^{2}}{{x}^{2}}+ax+1}-\sqrt{{{a}^{2}}{{x}^{2}}+1}$ is
	$\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{\tan x}}-{{e}^{x}}}{\tan x-x}=$
	If $f(x)=\sqrt{\frac{x-\sin x}{x+{{\cos }^{2}}x}}$ , then $\underset{x\to \infty }{\mathop{\lim }}\,f(x)$ is
	$\underset{x\to -1}{\mathop{\lim }}\,\frac{\sqrt{\pi }-\sqrt{{{\cos }^{-1}}x}}{\sqrt{x+1}}$ is given by