f-x-2ln-x-1-ln-2x-1-1-the-intersextion-Curve-with-axe-XX-2-find-the-equation-of-Circle-tengent-to-the-Curve-f-and-axe-O-Y-Y-gt-0-and-the-relative-maximum-of-f-x-3-the-Area-delimited

Question Number 203260 by a.lgnaoui last updated on 13/Jan/24

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2ln}\mid\mathrm{x}−\mathrm{1}\mid+\mathrm{ln}\left(\mathrm{2x}+\mathrm{1}\right) \\ $$$$\left.\bullet\mathrm{1}\right)−\mathrm{the}\:\mathrm{intersextion}\:\:\mathrm{Curve}\:\mathrm{with} \\ $$$$\mathrm{axe}\:\mathrm{XX}^{'} ? \\ $$$$\left.\bullet\mathrm{2}\right)−\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{Circle}\:\mathrm{tengent}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{Curve}\:\left(\mathrm{f}\right)\:\mathrm{and}\:\mathrm{axe}\:\left(\mathrm{O},\mathrm{Y}\right):\mathrm{Y}>\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{relative}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left.\bullet\mathrm{3}\right)−\mathrm{the}\:\mathrm{Area}\:\mathrm{delimited}\:\mathrm{by}\:\mathrm{x}=\mathrm{3} \\ $$$$\:\:\:\:\:\mathrm{max}\:\mathrm{relative}\:\mathrm{and}\:\mathrm{Circle}\:? \\ $$$$\left.\bullet\mathrm{4}\right)\mathrm{Graphe}\:\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

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