The limit \[\underset{x\to \infty }{\mathop{\lim }}\,x\left[ {{\tan }^{-1}}\left( \frac{x+1}{x+2} \right)-{{\tan }^{-1}}\left( \frac{x}{x+2} \right) \right]\]is equal to

The limit \[\underset{x\to \infty }{\mathop{\lim }}\,x\left[ {{\tan }^

1.	The limit \[\underset{x\to \infty }{\mathop{\lim }}\,x\left[ {{\tan }^{-1}}\left( \frac{x+1}{x+2} \right)-{{\tan }^{-1}}\left( \frac{x}{x+2} \right) \right]\]is equal to
A.	2
B.	\[\frac{1}{2}\]
C.	\[-\frac{1}{3}\]
D.	None of these
Answer» C. \[-\frac{1}{3}\]

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The limit \[\underset{x\to \infty }{\mathop{\lim }}\,x\left[ {{\tan }^{-1}}\left( \frac{x+1}{x+2} \right)-{{\tan }^{-1}}\left( \frac{x}{x+2} \right) \right]\]is equal to

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