Evaluate the following limits:

Question:

Evaluate the following limits:

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

 

Solution:

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

As x tends to 0, tan(x) also tends to zero,

So,

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

$=1$

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

 

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