If $0 \le f(x) \le M$, prove $\lim\limits_{n \to \infty} \left[ \int_0^1 f(t)^n \, dt \right]^{1/n} = M$
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?