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montrer-que-x-R-0-1-on-a-ln-x-x-1-lt-1-x-




Question Number 167482 by mathman1234 last updated on 17/Mar/22
montrer que ∀x∈R−{0; 1} on a  ((ln(x))/(x−1)) < (1/( (√x))) ?
$$\mathrm{montrer}\:\mathrm{que}\:\forall\mathrm{x}\in\mathbb{R}−\left\{\mathrm{0};\:\mathrm{1}\right\}\:\mathrm{on}\:\mathrm{a} \\ $$$$\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}−\mathrm{1}}\:<\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:? \\ $$

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