MCQ
$\lim \limits_{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{\frac{1}{x}}$ is equal to
- A$2$
- B$e$
- C$1$
- ✓$e^{2}$
$=\lim \limits_{x \rightarrow 0} \frac{1}{x}\left\{\tan \left(\frac{\pi}{4}+x\right)-1\right\}$
$=\lim \limits_{x \rightarrow 0}\left(\frac{1+\tan x-1+\tan x}{x(1-\tan x)}\right)$
$=e^{\lim \limits_{x \rightarrow 0} \frac{2 \tan x}{x(1-\tan x)}}$
$=e^{2}$
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