Question

The value of $\underset{n\to \infty }{lim}(1+\sin \frac{a}{n}{)}^n$ is :

• A. $1$
• B. $e^a$
• C. $e^{2a}$
• D. $e^{-a}$

Answer 1

The correct option is B $e^a$

$\begin{array}{c}{lim}_{n\to \infty }{\left(1+\sin \frac{a}{n}\right)}^n\\ ={lim}_{n\to \infty }n.\sin \frac{a}{n}\\ =e^{{lim}_{n\to \infty }}n.\frac{\sin \frac{a}{n}}{\frac{a}{n}}.\frac{a}{n}\\ =e^a\\ OptionBiscorrectanswer.\end{array}$