Mathematics-Online lexicon: Exponential Function

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	Mathematics-Online lexicon:
	Exponential Function

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The exponential function can be defined as the limit of a sequence or a series:

$\displaystyle e^x = \exp(x)$	$\displaystyle =$	$\displaystyle \lim_{n\to\infty} (1 + x/n)^{n}$
	$\displaystyle =$	$\displaystyle \sum_{n=0}^\infty \frac{1}{n!} x^n\, .$

The exponential function is positive for all $x\in\mathbb{R}$ and it satisfies the functional equality

$\displaystyle e^{x+y} = e^x e^y\, .$

In particular $e^{-x}=1/e^x$ .

Graph of the exponential function:

$\includegraphics{graph_exp}$

Annotation:

automatically generated 4/ 7/2008