Could someone prove this by the mean value theorem:

-ln(1-x) < x/(1-x) for 0 < x< 1

I got really close to it..

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- Apr 25th 2010, 09:19 AMMonster32432421Mean Value Theorem proof
Could someone prove this by the mean value theorem:

-ln(1-x) < x/(1-x) for 0 < x< 1

I got really close to it.. - Apr 25th 2010, 11:00 AMPlato
Use the mean value to prove Napier’s inequality: if $\displaystyle 0<a<b$ then $\displaystyle \frac{1}{b}\le\frac{\ln(b)-\ln(a)}{b-a}\le\frac{1}{a}$.

Then let $\displaystyle a=1-x~\&~b=1$. - Apr 26th 2010, 02:54 AMMonster32432421
why do you let a=1-x? not a=x

- Apr 26th 2010, 07:03 AMPlato
- Apr 26th 2010, 07:30 AMrebghb
(Already seen 2 posters posting the same question, interesting) :D