Let m and n be positive integers, c a positive real number. The following functions all tend to \infty as x \to \infty and they are arranged in order of increasing growth rate:

\ln(x), \! x^{1/m}, \! x^n, \! e^{cx}, \! e^{x^{n}}

(a) Where in the list would you place x^x and \frac{x}{\ln(x)}?
(b) Find a function which grows faster than any on the list.
(c) Find a function which grows more slowly than any on the list.