If \(x\) and \(y\) are distinct positive reals, prove the inequality

\[ \large \sqrt{xy} < \frac{y-x}{\ln(y) - \ln(x)} < \frac{x+y}2. \]

If \(x\) and \(y\) are distinct positive reals, prove the inequality

\[ \large \sqrt{xy} < \frac{y-x}{\ln(y) - \ln(x)} < \frac{x+y}2. \]

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TopNewestLet \(\large y=\displaystyle\lim _{ h\rightarrow 0 }{ x+h } \). – Rohit Ner · 1 year, 4 months ago

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