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.