Question

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

Answer 1

$\underset{x\to 0}{\lim }\left[\frac{e^{\tan x}-1}{\tan x}\right]$

If x → 0, then tan x → 0.

Let y = tan x

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