Here is the precise definition for a limit:[br]Let [math]f[/math] be defined on an open interval containing [math]c[/math] except possibly at [math]c[/math] itself. We say [br] [color=#333333]The limit of [/color][math]f\left(x\right)[/math][color=#333333] as [/color][math]x[/math][color=#333333] approaches [/color][math]c[/math][color=#333333] is the number [/color][math]L[/math][br]and we write[br] [math]\lim_{x\to c}f\left(x\right)=L[/math][br]if[br] For every number [math]\epsilon>0[/math], there is some number [math]\delta>0[/math] such that[br] [math]0<\left|x-c\right|<\delta\Rightarrow\left|f\left(x\right)-L\right|<\epsilon[/math].[br][br]The last mathematical expression above might be interpreted: Whenever [math]x[/math] is within [math]\delta[/math] of [math]c[/math] (but not actually equal to [math]c[/math]), [math]f\left(x\right)[/math] is within [math]\epsilon[/math] of [math]L[/math].[br][br]In this figure, a random [math]\epsilon[/math] will be given, and you must find a corresponding [math]\delta[/math]. [b]NOTE: you may have to zoom in the window to select a [/b][math]\delta[/math][b] that is small enough[/b]. As you zoom in, the slider to pick your [math]\delta[/math] will adjust.