Question Number 36750 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({t}\right)=\sum_{{n}\geqslant\mathrm{1}} \:\left(−\mathrm{1}\right)^{{n}} {ln}\left\{\mathrm{1}+\:\frac{{t}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\right\} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:\:{and}\:{uniform}\:{convergence} \\ $$$${of}\:\Sigma\:{f}_{{n}} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:{lim}_{{t}\rightarrow+\infty} \:{f}\left({t}\right)={ln}\left(\frac{\mathrm{2}}{\pi}\right)\:.…
Question Number 36748 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{ln}\left({nx}\right)} \\ $$$$\left.\mathrm{1}\left.\right)\:{give}\:{D}_{{f}} \:\:{and}\:{study}\:{f}\:{on}\right]\mathrm{1},+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continjity}\:{of}\:{f}\:{and}\:{calculate} \\ $$$${lim}\:_{{x}\rightarrow\mathrm{1}} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\…
Question Number 167819 by Mathspace last updated on 26/Mar/22 $${let}\:{f}\left({x}\right)={e}^{−{x}} {arctan}\left(\mathrm{2}{x}\right) \\ $$$${find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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…