Questions in fun-lim

Select	Question
	$\underset{x\to 0}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{b}^{x}}}{{{e}^{x}}-1}$ =
	If $f(x)\,={{\cot }^{-1}}\left( \frac{3x-{{x}^{3}}}{1-3{{x}^{2}}} \right)$ and $g(x)={{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$ , then $\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)\,-g(a)},$ $0<\,a < \frac{1}{2}$ is
	$\underset{x\to -2}{\mathop{\lim }}\,\frac{{{\sin }^{-1}}(x+2)}{{{x}^{2}}+2x}$ is equal to
	$\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+3}{x+1} \right)}^{x+1}}=$
	$\underset{x\to 0}{\mathop{\lim }}\,{{(1-ax)}^{\frac{1}{x}}}=$
	The value of $\underset{x\to 7}{\mathop{\lim }}\,\frac{2-\sqrt{x-3}}{{{x}^{2}}-49}$ is
	If $\underset{x\to 0}{\mathop{\lim }}\,\frac{\log (3+x)\,-\log (3-x)}{x}=k,\,$ then the value of k is
	If $\underset{x\to 0}{\mathop{\lim }}\,\frac{[(a-n)\,nx-\tan x]\sin nx}{{{x}^{2}}}=0,$ where n is non zero real number, then a is equal to
	Given that$f'$ (2)=6 and ${f}'(1)=4)=$ , then $\underset{h\to 0}{\mathop{\lim }}\,\frac{f(2h+2+{{h}^{2}})-f(2)}{f(h-{{h}^{2}}+1)-f(1)}=$
	$\underset{x\to 0}{\mathop{\lim }}\,\,\frac{{{e}^{x}}-{{e}^{-x}}}{\sin x}$ is