Q. The value of $\lim_{x \rightarrow 0}\frac{(1 - \cos{2x})}{x^{2}}$ is
A) Does not exist
B) Infinite
C) 0
D) 2
Explanation
(d)
$\lim_{x \rightarrow 0}\frac{\left( 1 - \cos{2x} \right)}{x^{2}}$
$= \lim_{x \rightarrow 0}\frac{2\sin^{2}x}{x^{2}}$
$= 2\lim_{x \rightarrow 0}{\left( \frac{\sin x}{x^{2}} \right)^{2} = 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.