Chapter 8.7, Problem 108E

To determine

To prove: That if $f\left(x\right)\ge 0,\underset{x\to a}{\lim }f\left(x\right)=0,$ and $\underset{x\to a}{\lim }g\left(x\right)=\infty ,then\underset{x\to a}{\lim }f{\left(x\right)}^{g\left(x\right)}=0$.