Questions in fun-lim

Select	Question
	$\underset{x\to \pi /6}{\mathop{\lim }}\,\left[ \frac{3\sin x-\sqrt{3}\cos x}{6x-\pi } \right]=$
	$\underset{x\to 0}{\mathop{\lim }}\,\frac{\cos (\sin x)-1}{{{x}^{2}}}=$
	$\underset{n\to \infty }{\mathop{\lim }}\,{{({{3}^{n}}+{{4}^{n}})}^{\frac{1}{n}}}=$
	If $\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}},$ then the values of a and b are
	$\underset{\theta \to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\frac{\pi }{2}-\theta }{\cot \theta }$ =
	$\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{4}{x-1} \right)}^{3x-1}}=$
	$\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{{{e}^{x}}-{{e}^{\sin x}}}{x-\sin x} \right]$ is equal to
	The value of $\underset{x\to -1}{\mathop{\lim }}\,\frac{{{x}^{2}}+3x+2}{{{x}^{2}}+4x+3}$ is equal to
	The value of $\underset{x\to 0}{\mathop{\lim }}\,\frac{2}{x}\log (1+x)$ is equal to
	The value of $\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{3x-4}{3x+2} \right)}^{\frac{x+1}{3}}}$ is equal to