Q. $\lim_{x \rightarrow 1}{(1 - x)\tan\left( \frac{\pi x}{2} \right)}$ is equal to
A) $\frac{\pi}{2}$
B) $\pi$
C) $\frac{2}{\pi}$
D) 0
Explanation
(c)
Put, $1 - x = y\ \ \ as\ \ \ \ x \rightarrow 1,\ y \rightarrow 0$
$\therefore\ \ \ \ \lim_{y \rightarrow 0}{y\tan\frac{\pi(1 - y)}{2}} = \lim_{y \rightarrow 0}{\frac{2}{\pi}\frac{\left( \frac{\pi y}{2} \right)}{\tan\left( \frac{\pi y}{2} \right)}} = \frac{2}{\pi}\ \ \ \$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.