Mathematik-Online lexicon: Removable Singularities

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	Mathematik-Online lexicon:
	Removable Singularities

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Example:

$\displaystyle f(x)$	$\displaystyle =\frac{x^3-3x^2-2x+6}{x^3-3x^2+x-3} \qquad D_{max}=\mathbb{R}\setminus \{3\}$
	$\displaystyle =\frac{(x-3)(x^2-2)}{(x-3)(x^2+1)}$

Check the point :

$\displaystyle \lim_{x \to 3 \textnormal{, } x>3}f(x)$	$\displaystyle =\frac{7}{10}$
$\displaystyle \lim_{x \to 3 \textnormal{, } x<3}f(x)$	$\displaystyle =\frac{7}{10}$

Thus there is a removable singularity at the point $(3/\frac{7}{10})$ .

$\includegraphics[width=0.8\textwidth]{luecke}$

(Authors: Jahn/Knödler)

see also:

automatisch erstellt am 8. 7. 2004