If limx→af(x)=l and limx→ag(x)=m, then limx→a(f(x))g(x)=l m
True
If both the limits limx→af(x) and limx→ag(x) exist finitely, then we can apply the limits independently to them in a limit involving both of them and x→a, provided the limit does not become indeterminate or infinite.
This is also true for taking exponents, like f(x)g(x).