Show that $\lim (\int_{a}^{b} f^n )^{\frac{1}{n}} = \sup(f(x))$
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?