find-lim-x-gt-0-e-x-x-1-x-2-

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

f i n d {l i m}_{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!} + \dots

\frac{e^{x} - x - 1}{x^{2}} = \frac{1}{2!} + \underset{i = 1}{\sum^{\infty}} \frac{x^{i}}{(i + 2)!}

\lim_{x \to 0} (. .) = \frac{1}{2}