The value of \[\underset{x\to 2}{\mathop{\lim }}\,\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}\]is

\[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\left[ 1-\tan \left( \frac{x}{2} \right) \right]\,[1-\sin x]}{\left[ 1+\tan \left( \frac{x}{2} \right) \right]\,{{[\pi -2x]}^{3}}}\]

The value of \[\underset{x\to 2}{\mathop{\lim }}\,\frac{\sqrt{1+\sqr

1.	The value of \[\underset{x\to 2}{\mathop{\lim }}\,\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}\]is
A.	\[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\left[ 1-\tan \left( \frac{x}{2} \right) \right]\,[1-\sin x]}{\left[ 1+\tan \left( \frac{x}{2} \right) \right]\,{{[\pi -2x]}^{3}}}\]
B.	\[\frac{1}{4\sqrt{3}}\]
C.	0
D.	None of these
Answer» B. \[\frac{1}{4\sqrt{3}}\]

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The value of \[\underset{x\to 2}{\mathop{\lim }}\,\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}\]is

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