Q. $\lim_{x \rightarrow 1}\frac{\tan{(x^{2} - 1)}}{x - 1}$ is equal to
A) 2
B) $\frac{1}{2}$
C) -2
D) $- \frac{1}{2}$
Explanation
(a)
We have, $\lim_{x \rightarrow 1}\frac{\tan\left( x^{2} - 1 \right)}{x - 1}$ $\left\lbrack \frac{0}{0}\ from \right\rbrack$
$= \lim_{x \rightarrow 1}\frac{\sec^{2}{\left( x^{2} - 1 \right).2x}}{1}$
[using L’Hospital’s rule]
$= 2.\sec^{2}{(0) = 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.