Explore the definition of the limit

for various values of epsilon including epsilon = 0.1.

Use the following LiveMath Notebook to determine what values of x makes the function y = |f(x) - 19| - 0.1 less than 0 near a = 2. You can change the value of epsilon and you can also explore with changing a and the function. View an animation to see how this can be done.

Acknowledgment: The first place which the author saw this way to approach this problem is in Jerry Johnson and Benny Evans' Discovering Calculus with Derive.