Good afternoon,
I am working on a problem that asks to find the following limit:
$\displaystyle
lim_{x\rightarrow\infty}(1+\frac{1}{x})^x
$
This should be equal to e, but I am having some difficulty remembering why.
I checked WolframAlpha and was provided with the following:
$\displaystyle
lim_{x\rightarrow\infty}(1+\frac{1}{x})^x
$
Indeterminate form of type $\displaystyle 1^\infty$. Transform using
$\displaystyle
lim_{x\rightarrow\infty}(1+\frac{1}{x})^x
$ = $\displaystyle
lim_{e^{x\rightarrow\infty}}x log(1+\frac{1}{x})
$
Where did this come from?