Prove by Mean Value Theorem $frac{x}{1+x}<ln(1+x)0$
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Prove for $x>0$ $$ frac{x}{1+x}<ln(1+x)<x $$ I tried writing $ln(1+x)=ln(1+x)-ln(1)$ and using the MVT for the $(1,1+x)$ interval. I eventually could prove the inequality but how do I have to prove even for $(0,1)$
calculus inequality logarithms
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edited Nov 18 at 6:35
Martin Sleziak
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asked Mar 18 '15 at 17:55
user224677
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