This is meant to demonstrate the epsilon-delta definition of a limit.
This shows the graph of the square root function, with x = 4 being sent to
y = 2.
What to do:
- Change the value of ε (epsilon) by clicking and dragging up or down the green spot
on the top edge of the epsilon region near the y-axis.
- Change the value of δ (delta) by clicking and dragging left or right the green spot on the right edge of the delta region near the x-axis.
- Change the value of x by clicking and dragging the green spot just above the number
(which is initially set at 4.567).
So with this diagram, you can see that if x is within δ units of 4, then y is
within ε units of 2.