Definition: [br]Given a function f and real numbers c and L, we say that [math]\frac{lim}{x\longrightarrow c}f\left(x\right)=L[/math] if and only if[br]for any [math]\varepsilon[/math] > 0 there exists a [math]\delta[/math] > 0 such that [br]if c - [math]\delta[/math] < x < c + [math]\delta[/math], x [math]\ne[/math] c then L - [math]\varepsilon[/math] < [math]f\left(x\right)[/math] < L + [math]\varepsilon[/math].[br][br]This applet is designed to give a graphical interpretation of this formal definition.[br][br]Enter a desired function into the input box for f(x).[br]Choose a value for c by typing into its input box.[br]Determine the appropriate value for the limit L and type it into its input box.[br]Choose a value for epsilon ([math]\varepsilon[/math]) by adjusting its slider or typing into its input box.[br]Choose an appropriate corresponding value for delta ([math]\delta[/math]) by adjusting its slider or typing into its input box.[br][br]If you can find an appropriate value of delta no matter how small the value of epsilon then you have demonstrated that the limit value L is correct.