Previous in Relation and Functions Next in Relation and Functions | ||
Question Number 33167 by abdo imad last updated on 11/Apr/18 | ||
$${f}\:{is}\:{a}\:{continue}\:{and}\:{positive}\:{function}\:{on}\:\left[{a},{b}\right]\:{with}\:{a}<{b} \\ $$ $${let}\:{m}\:={max}_{{x}\in\left[{a},{b}\right]} \:{f}\left({x}\right)\:{prove}\:{that} \\ $$ $${lim}_{{n}\rightarrow\infty} \:\:\left(\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:{f}^{{n}} \left({x}\right){dx}\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ | ||
Commented byabdo imad last updated on 12/Apr/18 | ||
$${prove}\:{that}\:{m}={lim}_{{n}\rightarrow\infty} \left(\:\frac{\mathrm{1}}{{b}−{a}}\int_{{a}} ^{{b}} \:{f}^{{n}} \left({x}\right){dx}\right)^{\frac{\mathrm{1}}{{n}}} \:. \\ $$ | ||