Epsilon-Delta Definition of a Limit - Case Study: f(x) = 1 if x>0, 0 if x < 0.

For the function f(x) = 1 if x > 0 and f(x) = 0 if x < 0, we saw before that the left and right hand limits are different. Try to find an ε for which no δ works. It only takes one such ε to show that the limit of f(x) at 0 does not equal L. Will other values of L work? Why or why not?

Use the sliders to change the values of δ and ε.

Jason McCullough, Created with GeoGebra