Question

The value of the ${lim}_{x\to 0}{\left(\frac{x}{\sin x}\right)}^{6/x^2}$ is -

• A. $1$
• B. $e^{-1}$
• C. $e^{-18}$
• D. $e^6$

Answer 1

The correct option is A $1$

$li{m}_{x\to 0}\left(\frac{1}{\frac{\sin x}{x}}\right)\times li{m}_{x\to 0}^{6/x^2}1\times e^{li{m}_{x\to 0}\frac{6-1}{x^2}}=e^{li{m}_{x\to 0}\frac{5}{x^2}}=e^0=1$