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Question Number 28095 by tawa tawa last updated on 20/Jan/18

$$\underset{x\to 0^{-}}{\lim }{(1+\mathrm{tanx})}^{-\mathrm{cotx}}$$

Commented by abdo imad last updated on 20/Jan/18

$$={lim}_{x\to 0^{-}}{e}^{-cotanxln(1+tanx)}but$$$$ln(1+tanx){}_{x\in V\left(0\right)}\sim tanx\Rightarrow -cotanxln(1+tanx)$$$$\sim -\frac{tanx}{tanx}=-1\Rightarrow {lim}_{x\to 0^{-}}{(1+tanx)}^{-cotanx}=\frac{1}{e}.$$

Commented by tawa tawa last updated on 21/Jan/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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