A Delta-Epsilon Applet
This Applet lets the student work with the Delta-Epsilon definition of
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.
Proving a limit means finding a rule that finds a delta for every
positive epsilon and proving that it works. For functions of the
level that we typically see in a calculus class, it is pretty
convincing to find a delta when epsilon is .1, .01, and .001, and to
use a picture to show that the deltas work.
