f is a continue and positive function on [a,b] with a<b let m =max_(x∈[a,b]) f(x) prove that lim_(n→∞) ( (1/(b−a)) ∫


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Question Number 33167 by abdo imad last updated on 11/Apr/18

$f i s a c o n t i n u e a n d p o s i t i v e f u n c t i o n o n [a, b] w i t h a < b$ $l e t m = {m a x}_{x \in [a, b]} f (x) p r o v e t h a t$ ${l i m}_{n \to \infty} {(\frac{1}{b - a} \int_{a}^{b} f^{n} (x) d x)}^{\frac{1}{n}}$
Commented byabdo imad last updated on 12/Apr/18

$p r o v e t h a t m = {l i m}_{n \to \infty} {(\frac{1}{b - a} \int_{a}^{b} f^{n} (x) d x)}^{\frac{1}{n}} .$
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