Saturday, 10 June 2017

calculus - Prove by Mean Value Theorem $frac{x}{1+x}

Prove for x>0
$$
\frac{x}{1+x}<\ln(1+x)
$$
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)

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