Question Number 36744 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}}\:{cos}^{{n}} \left({x}\right){sin}\left({nx}\right) \\ $$$$\left.\mathrm{1}\right){prove}\:{the}\:{convergence}\:{of}\:{this}\:{serie} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{f}\:{is}\:{C}^{\mathrm{2}} \:{on}\:{R}\:−\left\{{k}\pi,{k}\in{Z}\right\}{and} \\ $$$${calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{a}\:{exprrssion}\:{of}\:{f}.…
Question Number 36741 by prof Abdo imad last updated on 04/Jun/18 $${calculate}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{n}!} \\ $$ Commented by abdo.msup.com last updated on 05/Jun/18 $${S}\left({x}\right)={Im}\left(\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 36742 by prof Abdo imad last updated on 04/Jun/18 $${study}\:{the}\:{convergence}\:{of}\: \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} {ln}\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}\left(\mathrm{1}+{x}\right)}\right). \\ $$ Commented by maxmathsup by imad last…
Question Number 36661 by Tinkutara last updated on 03/Jun/18 Commented by Tinkutara last updated on 03/Jun/18 One-one or onto? Commented by Tinkutara last updated on 06/Jun/18 please help…
Question Number 102164 by mathmax by abdo last updated on 07/Jul/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:\:+\mathrm{3y}\:=\:\mathrm{e}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{2x}\right) \\ $$ Answered by mathmax by abdo last updated on…
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…