So I am currently going over some old calculus concepts and ran cross the exponential function expressed as a limit:
$$e^x = \lim_{n\rightarrow \infty}\left(\!1+\frac{x}{n}\!\right)^n $$
Where exactly does this come from? How can we show that this is true?
Additionally, I have also seen this:
$$e^x = \lim_{n\rightarrow 0}(1+xn)^{\frac{1}{n}} $$
How can we show that this is true?