hey i had a disagreement today with my prof
we were doing l'hopital's rule with
$$\lim_{x\to \infty}(1+x)^{\frac{1}{x}}$$
I said that the limit should be $$x \rightarrow o^{+}$$ not infinity in order for us to get e
what he did lead to $$e^{\lim_{x\to \infty}\frac{1}{1+x}}$$
which i said goes to 1 not e

Question

hey i had a disagreement today with my prof
we were doing l'hopital's rule with 
$$\lim_{x\to \infty}(1+x)^{\frac{1}{x}}$$
I said that the limit should be $$x \rightarrow o^{+}$$ not infinity in order for us to get e
what he did lead to $$e^{\lim_{x\to \infty}\frac{1}{1+x}}$$
which i said goes to 1 not e

rational · Answer

yes whats the exact question ?

xapproachesinfinity · Answer

as i said my prof said that that limit gives e
which is not true for me! i disagreed with him

anonymous · Answer

You're right, I believe your professor meant one of the following:
$$\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x=\lim_{x\to0}(1+x)^{1/x}=e$$

xapproachesinfinity · Answer

yeah exactly!