Q. ${\lim_{n \rightarrow \infty}\left( 1 + \sin\frac{a}{n} \right)}^{n}$ equals
A) $e^{a}$
B) $e$
C) $e^{2a}$
D) 0
Explanation
(a)
${\lim_{n \rightarrow \infty}\left( 1 + \sin\frac{a}{n} \right)}^{n} = e^{\lim_{n \rightarrow \infty}\frac{\sin{a/n}}{a/n.\ \frac{1}{a}}} = e^{a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.