Problem:
Consider the function

Illustrate graphically the epsilon-delta definition of limits to show that f is not continuous at x = 0.


Visualization:

At first glance, the following graph seems to show that f is continuous at x = 0.

However, after zooming in several times, the following graph provides evidence that f is not continuous at x = 0. The rectangle in this graph corresponds to choosing epsilon = 0.001.

These graphs were generated by Microcalc.


For this visualization, we have detailed instructions for the following software packages: