Question

$\underset{x\to \infty }{lim}\left[\left(x+2\right){\tan }^{-1}x-x{\tan }^{-1}x\right]=?$

• A. $\pi$
• B. $2$
• C. $1$
• D. $-1$

Answer 1

The correct option is A $\pi$

$\begin{array}{c}{lim}_{x\to \infty }\left[\left(x+2\right){\tan }^{-1}x-x{\tan }^{-1}x\right]\\ ={lim}_{x\to \infty }\left[x{\tan }^{-1}x+2{\tan }^{-1}x-x{\tan }^{-1}x\right]\\ ={lim}_{x\to \infty }\left[2{\tan }^{-1}x\right]\\ =2{\tan }^{-1}\infty \\ =2\times \frac{\pi }{2}=\pi \\ Hence,optionAisthecorrectanswer.\end{array}$