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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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 $\displaystyle a=1-x~\&~b=1$.
why do you let a=1-x? not a=x
Originally Posted by Monster32432421 why do you let a=1-x? not a=x Because $\displaystyle a=1-x$ gives us what we want. But $\displaystyle a=x$ does not.
(Already seen 2 posters posting the same question, interesting)
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