Evaluate the following limits:

Question:

Evaluate the following limits:

$\lim _{x \rightarrow 0} \frac{\left(e^{\tan x}-1\right)}{x}$

 

Solution:

$=\lim _{x \rightarrow 0} \frac{e^{\tan x}-1}{x}$

$=\lim _{x \rightarrow 0} \frac{e^{\tan x}-1}{x} \times \frac{\tan x}{\tan x}$

$=\lim _{x \rightarrow 0} \frac{e^{\tan x}-1}{\tan x} \times \frac{\tan x}{x}$

$=1 \times 1$

$=1$

$\therefore \lim _{x \rightarrow 0} \frac{e^{\tan x}-1}{x}=1$

 

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