This applet lets the student work with the epsilon-delta definition of a limit.

Recall that when we say the limit as x approaches a of f(x) is L we mean that for every epsilon > 0 there is a delta > zero with
|f(x) - L| < epsilon whenever 0 < | x-a | < delta.

This definition is often hard for students to understand, so it is useful to do a visual translation:  the limit as x approaches a of f(x) is L means for every height epsilon we can find a width delta so that for a box centered at (a,L) going up and down epsilon and right and left delta, the function only escapes through the sides of the box rather than the top and bottom.