I'm looking for a proof of the following statement:
If lim f(x) exists, then lim nth root [ f(x) ] = nth root [ lim f(x) ]
I can't seem to find a proof in any Calculus/Analysis books.
If $\displaystyle \lim f(x) > 0$, then this holds by the chain rule (the statement about the limit of composition) since $\displaystyle \sqrt[n]{x}$ is continuous for $\displaystyle x>0$.