Q. For $x \in R\ \ \lim_{x \rightarrow \infty}\left( \frac{x - 3}{x + 2} \right)^{x}$ is equal to
A) $e$
B) $e^{- 1}$
C) $e^{- 5}$
D) $e^{5}$
Explanation
(c)
$\lim_{x \rightarrow \infty}\left( \frac{x - 3}{x + 2} \right)^{x} = \lim_{x \rightarrow \infty}\left\lbrack \frac{1 - \frac{3}{x}}{1 + \frac{2}{x}} \right\rbrack^{x}$
$= \frac{e^{- 3}}{e^{2}} = e^{- 5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.