# delta epsilon limits

- Author:
- Lenore Horner

- Topic:
- Limits

This applet illustrates the formal definition of a limit. The limit as x approaches A of f(x) is C if for any epsilon (illustrated by the vertical red bar) you can find a delta (illustrated by the width of the blue band at the x-axis) such that all values D within that blue band yield y values within epsilon of the limit (within the red band).
The arrow will turn on the animation of the move slider so that D moves from A-delta to A+delta. Check that the resulting y-values are always between C-epsilon and C+epsilon.