Q. The value of $\lim_{x \rightarrow 0}\frac{5^{x} - 5^{- x}}{2x}$ is
A) $\log 5$
B) 0
C) 1
D) $2\log 5$
Explanation
(a)
$\lim_{x \rightarrow 0}\frac{5^{x} - 5^{- x}}{2x} = \lim_{x \rightarrow 0}\frac{5^{x}\log 5 - 5^{- x}\log 5}{2}$
[by L’ Hospital’s rule]
$= \frac{\log{5 + \log 5}}{2}$
$= \log 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.