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[不等式] (z)恒成立问题

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realnumber Posted at 2014-4-25 11:53:39 |Read mode
李明:想知道实数p取值在什么范围,能使得f(x)≥0对于x>0成立!
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 Author| realnumber Posted at 2014-4-25 12:03:56
Last edited by realnumber at 2014-4-25 12:23:00当$x=\frac{1}{e}$时,显然成立.
当$x>\frac{1}{e}$时,$1+x+x\ln{x}+\frac{1}{1+\ln{x}}\ge p$.
当$0<x<\frac{1}{e}$时,$1+x+x\ln{x}+\frac{1}{1+\ln{x}}\le p$.其中$1+x+x\ln{x}+\frac{1}{1+\ln{x}}<1$显然.
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$type lm1.gsp (3.02 KB, Downloads: 3622)
$1\le p\le x_0$,$x_0$约为2.904......

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