Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

${lim}_{x\to 0}{\left(\frac{x}{sinx}\right)}^{6/x^2}{e}^{{lim}_{x\to 0}\frac{6}{x^2}\left(\frac{x-sinx}{sinx}\right)}{lim}_{x\to 0}\frac{6}{x^2}\left[\frac{x-(x-\frac{x^3}{3!})}{x}\right]=e$