Question

$\text{The limiting value of}{\left(cosx\right)}^{1/sinx}\text{as x}\to 0is$

• A. 1
• B. e
• C. 0
• D. 1/e

Answer 1

The correct option is A

1

${lim}_{x\to 0}(cosx{)}^{1/sinx}$
Given form is of $\left(1^{\infty }\right)$
= $e^{\underset{x\to 0}{lim}\frac{cosx-1}{sinx}}=e^{\underset{x\to 0}{lim}(-tan\frac{x}{2})}=e^0=1$