Mathematics-Online lexicon: Removable Singularities

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	Mathematics-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

A function

has a removable singularity at the point $x=x_{0}$ if the domain is a subset of $D_{max}=\mathbb{R}\setminus \{x_{0}\}$ and if the limit

$\displaystyle \lim_{x \to x_{0}}f(x)$

exists.

One has to verify that the limit from the right coincides with the limit from the left.

$\displaystyle \lim_{x \to x_{0} \textnormal{, } x>x_{0}}f(x)\quad=\lim_{x \to x_{0} \textnormal{, } x<x_{0}}f(x)=c\qquad c \in \mathbb{R}$

Then the function has a removable singularity at the point $(x_{0}/c)$ . Usually one mark this removable singularity with an empty box in the sketch.

(Authors: Jahn/Knödler)

see also:

automatically generated 7/ 8/2004