+9665 What is \(\displaystyle\lim_{x\rightarrow 0}\dfrac{\displaystyle\int^{x}_{0}{e^{t}}^{2}\mathtt{dt}}{x}\)
I know I am supposed to use L'Hópital's rule, but how??
+118658 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.
