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Question Number 27787 by abdo imad last updated on 14/Jan/18

$$find{lim}_{x->0}\frac{e^x-x-1}{x^2}.$$

Answered by prakash jain last updated on 14/Jan/18

$$e^x=1+x+\frac{x^2}{2!}+...$$ $$\frac{e^x-x-1}{x^2}=\frac{1}{2!}+\underset{i=1}{\sum ^{\mathrm{\infty }}}\frac{x^i}{(i+2)!}$$ $$\underset{x\to 0}{\lim }(..)=\frac{1}{2}$$

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