Q. $\lim_{x \rightarrow 0}\frac{\sin{|x|}}{x}$ is equal to
A) 1
B) 0
C) positive infinity
D) does not exist
Explanation
(d)
LHL$= \lim_{x \rightarrow 0}\frac{- \sin x}{x}$
$= - 1$
RHL$= \lim_{x \rightarrow 0}\frac{\sin x}{x}$
$= 1$
$\Rightarrow \ \ \ \ \ \ \ \ \ LHL \neq RHL$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \lim_{x \rightarrow 0}\frac{\sin{|x|}}{x}$ Does not exist.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.