Visual Calculus - Limits and Greatest Integer Function

Problem:
Explore the limits of the functions

g(x) = x^a [[1/x]]

as x approaches 0 for various values of a. f(x) = [[x]] is the greatest integer function or floor function which is the largest integer less than or equal to x.

Visualization:
Use the following LiveMath Notebook to change the values of a. View an animation to see how this can be done.

For what values of a does the limit of g(x), as x approaches 0, exist? Answer.