Exploring the epsilon-delta definition of limit
Move the slider to position point a.
Use the slider to choose a value of ε, and click the box to see the strip of y-values that are less than ε units from L.
Use the slider to try to find a value of δ with the property that whenever x is less than δ units from a, then f(x) (the y-value on the graph of f(x)) will be less than ε units from L. Click the box to see the strip of x-values that are less than δ units from a. Look at the rectangle defined by the strip of x-values and the strip of y-values. If the graph of the function is green inside that rectangle, then you have chosen an appropriate value of δ.
Barbara D'Ambrosia, Created with GeoGebra