Question Number 34863 by a.i msup by abdo last updated on 12/May/18 $${let}\:{f}\left({x}\right)=\:\frac{{artan}\left({x}+\mathrm{1}\right)}{\mathrm{1}+\mathrm{2}{x}} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by math khazana by abdo last updated…
Question Number 34849 by math khazana by abdo last updated on 11/May/18 $${let}\:{f}\left({x}\right)\:=\:\:\:\:\frac{{e}^{−{x}} }{\mathrm{2}+{x}} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$ Commented by math khazana by abdo last…
Question Number 165870 by neinhaltsieger last updated on 09/Feb/22 $$\: \\ $$$$\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{3}\right)\:=\:\sqrt{\boldsymbol{\mathrm{x}}\:−\:\mathrm{5}},\:\:\boldsymbol{\mathrm{f}}\left(\sqrt{\mathrm{21}}\right)\:=\:? \\ $$$$\: \\ $$ Answered by eman_64 last updated on 09/Feb/22 $$\:\:\:\:\boldsymbol{{x}}^{\mathrm{2}}…
Question Number 165848 by leonhard77 last updated on 09/Feb/22 $$\:{f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left(\mathrm{1}−{x}\right)={x} \\ $$$$\:\:{f}\left({x}\right)=? \\ $$ Answered by qaz last updated on 10/Feb/22 $$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{x}}−\mathrm{f}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right) \\…
Question Number 34774 by abdo mathsup 649 cc last updated on 11/May/18 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{n}^{{p}} \:{sin}^{\mathrm{2}} \left({n}!\right)}{{n}^{{p}+\mathrm{1}} }\:\:{with}\mathrm{0}<{p}<\mathrm{1}\:. \\ $$ Commented by abdo mathsup 649 cc…
Question Number 34770 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{f}\left({x}\right)=\:{ln}\left(\mathrm{1}+{ix}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{extrsct}\:{Re}\left({f}\left({x}\right)\right)\:{and}\:{Im}\left({f}\left({x}\right)\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{f}^{'} \left({x}\right)\:{by}\:{two}\:{methods} \\ $$ Commented by…
Question Number 34736 by math khazana by abdo last updated on 10/May/18 $${letf}\left({x}\right)=−\mathrm{2}{x}\:\:+\sqrt{{x}−\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right)\:\:\:{and}\:\left({f}^{−\mathrm{1}} \right)^{,} \left(\mathrm{2}\right) \\ $$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:−\mathrm{2}{x}+\mathrm{3}…
Question Number 34721 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:\xi\left({x}\right)\:=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:{with}\:{x}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:\:\frac{\mathrm{1}}{{x}−\mathrm{1}}\:\leqslant\xi\left({x}\right)\leqslant\:\frac{{x}}{{x}−\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{x}\rightarrow\mathrm{1}^{+} } \left({x}−\mathrm{1}\right)\xi\left({x}\right)\:. \\ $$ Terms…
Question Number 34719 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\Gamma\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:{with}\:{n}\:\in{N}. \\ $$ Commented by abdo mathsup 649 cc last updated on 12/May/18…
Question Number 100236 by mathmax by abdo last updated on 25/Jun/20 $$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} }{\left(\mathrm{k}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last…