Q. $\lim_{x \rightarrow \infty}\left( 1 - \frac{4}{x - 1} \right)^{3x - 1}$ is equal to
A) $e^{12}$
B) $e^{- 12}$
C) $e^{4}$
D) $e^{3}$
Explanation
(b)
$\lim_{x \rightarrow \infty}\left( 1 - \frac{4}{x - 1} \right)^{3x - 1} = \lim_{x \rightarrow \infty}\left\lbrack \left( 1 - \frac{4}{x - 1} \right)^{\frac{- (x - 1)}{4}} \right\rbrack^{- 4\left( \frac{3x - 1}{x - 1} \right)}$
$= e^{- 4\lim_{x \rightarrow \infty}(3 - 1/x)(1 - 1/x)} = e^{- 12}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.