Q. $\lim_{x \rightarrow \infty}\left( \frac{x^{2} + 5x + 3}{x^{2} + x + 2} \right)^{x}$ is equal to
A) $e^{4}$
B) $e^{2}$
C) $e^{3}$
D) $e$
Explanation
(a)
$\lim_{x \rightarrow \infty}\left\lbrack 1 + \frac{4x + 1}{x^{2} + x + 2} \right\rbrack^{x} = \lim_{x \rightarrow \infty}e^{\ \lim_{x \rightarrow \infty}\ \frac{4x^{2} + x}{x^{2} + x + 2}} = e^{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.