If a function [math]\large f[/math] is defined on an open interval containing [math]\large a[/math], except possibly not defined at [math]\large a[/math], we say the limit of [math]\large f(x)[/math] as [math]\large x[/math] approaches [math]\large a[/math] is [math]\large L[/math], written[br][center][math]\Large \lim_{x \to a} f(x)=L[/math],[/center]if for any number [math]\large \epsilon>0[/math], there exists a number [math]\large \delta>0[/math] such that [br][br][center]if [math]\Large |x - a| < \delta[/math], then [math]{\Large |f(x) -L|< \epsilon[/math],[/center]which is equivalent to [br][center]if [math]\Large a- \delta < x < a + \delta[/math] then [math]\Large L-\epsilon < f(x) < L+ \epsilon[/math]. [/center]