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acarchau
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 An inequality   « on: Dec 14th, 2008, 9:48pm » Quote Modify

Prove/disprove, for x>=0
(1+x)^(1+x) >= 1+x+x^2
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towr
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 Re: An inequality   « Reply #1 on: Dec 15th, 2008, 1:38am » Quote Modify

take
f(x) = (1+x)^(1+x)
g(x) = 1+x+x^2
then
f(0)=g(0)
f'(0)=g'(0)
f''(x) >= g''(x) for x>=0
so (since they are continuous) f(x) >= g(x) for x>=0
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ThudnBlunder
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 Re: An inequality   « Reply #2 on: Dec 15th, 2008, 3:30am » Quote Modify

Binomial Theorem.
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