Q. $\lim_{x \rightarrow 1}{\cos^{- 1}\left( \frac{1 - \sqrt{x}}{1 - x} \right)}$ is equal to
A) $\frac{\pi}{3}$
B) $\frac{\pi}{6}$
C) $\frac{\pi}{2}$
D) $\frac{\pi}{4}$
Explanation
(a)
$\lim_{x \rightarrow 1}{\cos^{- 1}\left( \frac{1 - \sqrt{x}}{1 - x} \right)}$
$= \lim_{x \rightarrow 1}{\cos^{- 1}\left( \frac{1 - \sqrt{x}}{\left( 1 - \sqrt{x} \right)\left( 1 + \sqrt{x} \right)} \right)}$
$= \lim_{x \rightarrow 1}{\cos^{- 1}\left( \frac{1}{1 + \sqrt{x}} \right)}$
$= \cos^{- 1}\left( \frac{1}{2} \right)$
$= \frac{\pi}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.