Q225 / 270 · NDA 2018 (Phase 2) · Mathematics

If the function $f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x}$ is continuous at each point in its domain, then what is the value of $f(0)$ ?

  • A
    -1/3
  • Correct answer
    B
    1/3
  • C
    2/3
  • D
    2

Solution

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

Hence, the correct answer is option: 'B'.

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