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$\lim _{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}=$
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$e^2$
$\begin{aligned} \text { Given limit } & =\lim _{x \rightarrow 0}\left(\frac{1+\tan x}{1-\tan x}\right)^{1 / x} \\ & =\lim _{x \rightarrow 0} \frac{\left\{(1+\tan x)^{1 / \tan x}\right\}^{(\tan x) / x}}{\left\{(1-\tan x)^{1 / \tan x}\right\}^{(\tan x) / x}}=\frac{e}{e^{-1}}=e^2 .\end{aligned}$
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