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   An inequality
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   Author  Topic: An inequality  (Read 1052 times)
acarchau
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An inequality  
« on: Dec 14th, 2008, 9:48pm »
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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 »
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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 »
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Binomial Theorem.
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