Question

If $\underset{x\to 0}{lim}(1+a\sin x{)}^{cosecx}=3,$ then a is

• A. In 2
• B. In 3
• C. In 4
• D. $e^3$

Answer 1

The correct option is B In 3

$3=\underset{x\to 0}{lim}(1+a\sin x{)}^{cosecx}$
$\left[1^{\infty }form\right]\Rightarrow \underset{x\to 0}{lim}{e}^{cosecx.a\sin x}=e^a$
$\therefore e^a=3\Rightarrow a={\log }_{e}3=ln3.$