Question

$\underset{x\to 0}{\lim }\frac{e^{\tan x}-1}{x}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{e^{\tan x}-1}{x}\right] \\ =\underset{x\to 0}{\lim }\left[\frac{e^{\tan x}-1}{\tan x}\times \frac{\tan x}{x}\right] \\ =1\times 1 \end{gathered}$$