Epsilon-Delta Definition for Limits
This applet gives a zoomed in look at part of the function .  The window is  and .  The point  is our specific .
You can let  take on values from 0.1 down to 0.005 using the slider.  Notice how the value for  changes to always create an interval on the -axis  such that any value of  chosen within that interval leads to a value  that is within the appropriate interval  on the -axis.