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Question Number 27789 by abdo imad last updated on 14/Jan/18

$$find{lim}_{x->0}{(1+sinx)}^{\frac{1}{x}}.$$

Commented byabdo imad last updated on 15/Jan/18

$$wehave{(1+sinx)}^{\frac{1}{x}}=e^{\frac{1}{x}ln(1+sinx)}$$ $$butforx\in V\left(0\right)sinx\sim xand$$ $$ln(1+sinx)\sim ln(1+x)\sim x\Rightarrow$$ $$\frac{ln(1+sinx)}{x}\sim 1\Rightarrow {lim}_{x->0}{(1+sinx)}^{\frac{1}{x}}=e.$$

Commented byprakash jain last updated on 16/Jan/18

$$\mathrm{thanks}.\mathrm{your}\mathrm{question}\mathrm{and}\mathrm{solution}$$ $$\mathrm{are}\mathrm{great}\mathrm{learning}\mathrm{experience}$$

Commented byabdo imad last updated on 16/Jan/18

$$thsnkyoufriendprakash...$$

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