Q. $\lim_{x \rightarrow 0}\frac{\int_{0}^{x^{2}}{\tan{\sqrt{t}\ dt}}}{x^{3}}$ is equal to
A) $\frac{2}{3}$
B) $\frac{3}{2}$
C) 1
D) None of these
Explanation
(d)
$\lim_{x \rightarrow 0}\frac{2x\tan{|x|}}{3x^{2}} = \frac{2}{3}\lim_{x \rightarrow 0}\frac{\tan{|x|}}{x}$
RHL is $\frac{2}{3}$ and LHL is $- \frac{2}{3}$
So, limit does not exist
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.