If the function `f(x)=(2x-sin^(-1)x)/(2x+tan^(-1)x)` is continuous at each point of its domain, then the value of `f(0)`
(A) `4/3` (B) `1/3` (C) `-1/3` (D) `2/3`

Answer

Option (B)
`1/3`

Explanation

\begin{aligned}
&f(0)=\lim _{x \rightarrow 0} \frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \\ \\
&=\lim _{x \rightarrow 0} \frac{2-\frac{\sin ^{-1} x}{x}}{2+\frac{\tan ^{-1} x}{x}}=\frac{2-1}{2+1}=\frac{1}{3}
\end{aligned}