f-x-xe-1-x-Prove-that-lim-n-n-1-0-f-x-n-dt-pi-2-

Tinku Tara June 3, 2023 Limits 0 Comments

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Question Number 140381 by Willson last updated on 07/May/21

f(x)=xe^(1−x) Prove that lim_(n→+∞) (√n) ∫^( 1) _0 [f(x)]^n dt = (√(π/2))

f (x) = {xe}^{1 - x}

Prove that \lim_{n \to + \infty} \sqrt{n} {\int_{0}}^{1} {[f (x)]}^{n} dt = \sqrt{\frac{π}{2}}

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