Q. The function $f(x)$ is defined as$f(x) = \frac{2x - \sin^{- 1}x}{2x + \tan^{- 1}x}$, if $x \neq 0$. The value of $f$ to be assigned at $x = 0$ so that the function is continuous there, is
A) $- \frac{1}{3}$
B) 1
C) $\frac{2}{3}$
D) $\frac{1}{3}$
Explanation
(d)
$f(0) = \lim_{x \rightarrow 0}\frac{2x - \sin^{- 1}x}{2x + \tan^{- 1}x}$
$= \lim_{x \rightarrow 0}\frac{2 - \frac{\sin^{- 1}x}{x}}{2 + \frac{\tan^{- 1}x}{x}}$
$= \frac{2 - 1}{2 + 1} = \frac{1}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.