This applet gives a zoomed in look at part of the function [math]f\left(x\right)=\frac{3}{2}x[/math]. The window is [math]X\left[1.9,2.1\right]_{0.02}[/math] and [math]Y\left[2.8,3.2\right]_{0.1}[/math]. The point [math]\left(2,3\right)[/math] is our specific [math]\left(c,L\right)[/math].[br][br]You can let [math]\epsilon[/math] take on values from 0.1 down to 0.005 using the slider. Notice how the value for [math]\delta[/math] changes to always create an interval on the [math]x[/math]-axis [math]\left(c-\delta,c+\delta\right)[/math] such that any value of [math]x[/math] chosen within that interval leads to a value [math]f\left(x\right)[/math] that is within the appropriate interval [math]\left(L-\epsilon,L+\epsilon\right)[/math] on the [math]y[/math]-axis.