Chapter 4.4, Problem 86E

Suppose f is a positive function. If ${\lim }_{x\to a}f(x)=0$ and ${\lim }_{x\to a}g(x)=\infty$, show that

$\underset{x\to a}{\lim }{[f(x)]}^{g(x)}=0$

This shows that 0^∞ is not an indeterminate form.