Explore graphically the limit of

as x approaches a for various values of a and n.

In the following Mathview Notebook, you can see the graph of y = f(x) in blue.

Explore with changing n; consider n = 4, 5, 10, 11. Can you detect a pattern?

You can also enter fractions; consider n = 1/3, 2/3, 1/4. It may not appear that there is a vertical asymptote for some of these values. Zoom in by making the x coordinates smaller but keeping the y-coordinates the same.