Limits question.

Two approaches below.  One uses L'Hopital and one uses a series expansion:

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Hi Max :)

someone better check this but I think.

$\displaystyle\lim_{x\rightarrow 0}\dfrac{\displaystyle\int^{x}_{0}{e^{t}}^{2}\mathtt{dt}}{x}\\ =\displaystyle\lim_{x\rightarrow 0}\dfrac{\left[{e^{t}}^{2}\right]_0^x}{1}\\ =\displaystyle\lim_{x\rightarrow 0}\left[{e^{t}}^{2}-e^0\right]\\ =\displaystyle\lim_{x\rightarrow 0}\left[{e^{t}}^{2}-1\right]\\ =e^0-1\\ =0$

Are you sure you were asked to use L'Hopital's Rule for this one?  L'Hopital's Rule considers the ratio of two functions of the same variable. You have a function of e on the numerator and a function of X on the denominator here.

Thanks all for answering :)

Stuck at this question on an online exercise.