Explore the limits of the functions

g(x) = xa [[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.

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.