Q. $\lim_{x \rightarrow 0}\left\lbrack \frac{\sqrt{a + x} - \sqrt{a - x}}{4x} \right\rbrack$ is equal to
A) $\frac{1}{2\sqrt{a}}$
B) $\frac{1}{4\sqrt{a}}$
C) $\frac{1}{3\sqrt{a}}$
D) $\frac{2}{\sqrt{a}}$
Explanation
(b)
$\lim_{x \rightarrow 0}\left\lbrack \frac{\sqrt{a + x} - \sqrt{a - x}}{4x} \right\rbrack$
$= \lim_{x \rightarrow 0}\left\lbrack \frac{a + x - a + x}{4x(\sqrt{a + x} + \sqrt{a - x})} \right\rbrack$
$= \lim_{x \rightarrow 0}\left\lbrack \frac{2x}{4x(\sqrt{a + x} + \sqrt{a - x})} \right\rbrack$
$= \frac{1}{4\sqrt{a}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.