# Math Help - Limit of the nth root of a function

1. ## Limit of the nth root of a function

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.

2. ## Re: Limit of the nth root of a function

If $\lim f(x) > 0$, then this holds by the chain rule (the statement about the limit of composition) since $\sqrt[n]{x}$ is continuous for $x>0$.