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delta epsilon 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.