Question Number 102162 by mathmax by abdo last updated on 07/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}+\mathrm{1}}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integer}\:\mathrm{serie} \\ $$ Terms of Service Privacy Policy…
Question Number 101998 by mathmax by abdo last updated on 06/Jul/20 $$\left.\mathrm{1}\right)\mathrm{solve}\:\mathrm{inside}\:\mathrm{C}\:\:\mathrm{x}^{\mathrm{n}} −\mathrm{e}^{−\mathrm{in}\alpha} \:=\mathrm{0}\:\:\:\:\:\left(\alpha\:\mathrm{real}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{let}\:\mathrm{P}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{n}} −\mathrm{e}^{−\mathrm{in}\alpha} \:\:\mathrm{factorize}\:\mathrm{P}\left(\mathrm{x}\right)\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{2}\right)\:\mathrm{decompose}\:\mathrm{inside}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{thefraction}\:\mathrm{F}\:=\frac{\mathrm{1}}{\mathrm{P}\left(\mathrm{x}\right)} \\ $$$$\mathrm{and}\:\mathrm{deyermine}\:\int\:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Terms…
Question Number 36442 by abdo mathsup 649 cc last updated on 02/Jun/18 $${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{2}+{x}^{\mathrm{2}} \:}\:\:\:−{x} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{f}\left({x}\right)}{{x}}\:{and}\:\:{lim}_{{x}\rightarrow−\infty} \:\frac{{f}\left({x}\right)}{{x}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{f}^{'} \left({x}\right)\:{and}\:{determine}\:{its}\:{sign}…
Question Number 36367 by chakraborty ankit last updated on 01/Jun/18 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$…
Question Number 36179 by prof Abdo imad last updated on 30/May/18 $${let}\:{f}\left({x},{y}\right)\:=\:\frac{{xy}}{{x}+{y}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){calcule}\:{x}\frac{\partial{f}}{\partial{x}}\left({x},{y}\right)\:+{y}\:\frac{\partial{f}}{\partial{y}}\left({x},{y}\right)\:{interms}\:{of}\:{f}\left({x},{y}\right) \\ $$ Commented by maxmathsup by imad last updated…
Question Number 36104 by rahul 19 last updated on 28/May/18 $$\mathrm{If}\:\boldsymbol{\mathrm{f}}:\boldsymbol{\mathrm{R}}\rightarrow\boldsymbol{\mathrm{R}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid\:\mathrm{f}\left({x}\right)\:−\:\mathrm{f}\left(\mathrm{y}\right)\mid\:\leqslant\:\mid\:\mathrm{sin}\:{x}\:−\:\mathrm{sin}\:\mathrm{y}\:\mid\forall{x},\mathrm{y}\in\mathbb{R}, \\ $$$$\mathrm{Then}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Bijective} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{many}−\mathrm{one} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{periodic} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{non}−\mathrm{periodic} \\ $$…
Question Number 101595 by mathmax by abdo last updated on 03/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{cos}^{\mathrm{n}} \mathrm{x} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{detemine}\:\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by…
Question Number 36010 by abdo mathsup 649 cc last updated on 27/May/18 $${let}\:{f}\left({x}\right)=\:\:\frac{{x}}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by prof Abdo…
Question Number 35988 by abdo mathsup 649 cc last updated on 26/May/18 $${let}\:{f}\left({x}\right)\:=\:\frac{{x}+\mathrm{2}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$ Commented by abdo mathsup…
Question Number 35986 by abdo mathsup 649 cc last updated on 26/May/18 $${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{1}\:+{n}\:{x}^{\mathrm{2}} }\:\:\:−{nx}\:+\mathrm{3}\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{the}\:{equation}\:{of}\:{assymptote}\:{of}\:{f}\:{at} \\ $$$${point}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right)\:.…