1. ## Continuity and integrability

Let fbe continuous and non-negative on [a,b]. Show that

$(\int_{a}^{b} f^{p})^{1/p} \rightarrowsup f(x)$ as $p\rightarrow\infty$

2. You mean $(\int_{a}^{b} f^{p})^{1/p} \rightarrow \underset{a \leq x \leq b}{\mbox{sup}} f(x)$.

What did you try? Do you have an idea why it's true?