$e^{\displaystyle x}$
$e^{\displaystyle x}$ $\,=\,$ $1$ $+$ $\dfrac{x}{1!}$ $+$ $\dfrac{x^2}{2!}$ $+$ $\dfrac{x^3}{3!}$ $+$ $\dfrac{x^4}{4!}$ $+$ $\cdots$ $+$ $\infty$
$e^{\displaystyle x}$ $\,=\,$ $\displaystyle \lim_{n\,\to\,\infty}{\Big(1+\dfrac{x}{n}\Big)^{\displaystyle n}}$
$\dfrac{d}{dx}{e^{\displaystyle x}} \,=\, e^{\displaystyle x}$
$\displaystyle \int{e^{\displaystyle x}}\,dx \,=\, e^{\displaystyle x}+c$
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