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[obm-l] Olimpiada colombiana universitaria
- To: obm-l@xxxxxxxxxxxxxx
- Subject: [obm-l] Olimpiada colombiana universitaria
- From: Joÿffffe3o Silva <d79i3mn8@xxxxxxxxxxxx>
- Date: Mon, 30 Apr 2007 13:48:24 -0300 (ART)
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"n"é um inteiro positivo e f : [0,1] -> R uma função contínua tal que:
integral[(x^k)f(x)]dx = 1 para k = 0, 1, ..., n-1.
Prove que f existe e que:
integral[(f(x))^2]dx >= n^2.
Os limites de integração são de 0 até 1 em todas as integrais anteriores.
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