# 4. Prove that the function $f (x) = x^n$ is continuous at x = n, where n is a positive integer

$f (x) = x^n$
the function $f (x) = x^n$ is defined for all positive integer, n
$f(n) = n^n\\ \lim_{x\rightarrow n}f(x) = n^n\\ \lim_{x\rightarrow n}f(x) = f(n)$
Hence,  the function $f (x) = x^n$ is continuous at x = n, where n is a positive integer