$\lim _{x \rightarrow 0} \frac{a^x-1}{\sin (x)}=$

Question

Aicharya · Accepted Answer

$\lim _{x \rightarrow 0} \frac{a^x-1}{\sin x}=\frac{\lim _{x \rightarrow 0} \frac{a^x-1}{x}}{\lim _{x \rightarrow 0} \frac{\sin x}{x}}=\frac{\log _e a}{1}=\log _e a$ Hence, option (a) is correct.

\(\lim _{x \rightarrow 0} \frac{a^x-1}{\sin (x)}=\)

Solution