Q. $\lim_{x \rightarrow 0}\left\lbrack \frac{3^{x} + 3^{- x} - 2}{x^{2}} \right\rbrack$ is equal to
A) $2\log 3$
B) $- \left( \log 3 \right)^{2}$
C) $- 2\log 3$
D) $\left( \log 3 \right)^{2}$
Explanation
(d)
$\lim_{x \rightarrow 0}\left\lbrack \frac{3^{x} + 3^{- x} - 2}{x^{2}} \right\rbrack$
$= \lim_{x \rightarrow 0}\frac{\left\lbrack \begin{array}{r}
1 + x\log 3 + \frac{x^{2}}{2!}\left( \log 3 \right)^{2} + \ldots + \\
1 - x\log 3 + \frac{x^{2}}{2!}\left( \log 3 \right)^{2} - ... - 2
\end{array} \right\rbrack}{x^{2}} = \left( \log 3 \right)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.