Question Number 34309 by prof Abdo imad last updated on 03/May/18 $${let}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} \:−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{radius}\:{of}\:{convergence} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{the}\:{sum}\:\:{S}\left({x}\right). \\ $$ Commented by…
Question Number 99839 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{let}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1}\:\mathrm{and}\:\mathrm{x}_{\mathrm{n}+\mathrm{1}} =\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}_{\mathrm{n}} } −\mathrm{x}_{\mathrm{n}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{x}_{\mathrm{n}} \:\rightarrow\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\mathrm{prove}\:\mathrm{that}\:\Sigma\:\mathrm{x}_{\mathrm{n}} \:\mathrm{converges}\:\mathrm{and}\:\mathrm{ddyermine}\:\mathrm{its}\:\mathrm{sum} \\ $$…
Question Number 99832 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{solve}\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{''} \:−\mathrm{xy}^{'} \:+\mathrm{2y}\:=\mathrm{x}^{\mathrm{3}} \mathrm{e}^{−\mathrm{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99828 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{let}\:\mathrm{A}\:=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\mathrm{determine}\:\mathrm{cosA}\:\mathrm{and}\:\mathrm{sinA} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{chA}\:\mathrm{and}\:\mathrm{shA} \\ $$ Commented by bachamohamed last updated…
Question Number 99822 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ch}\left(\mathrm{sinx}\right)}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99819 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{sove}\:\:\mathrm{sinx}\:\mathrm{y}^{'} \:−\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{y}\:=\mathrm{xe}^{−\mathrm{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34267 by math khazana by abdo last updated on 03/May/18 $${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{e}^{{x}} \right)\left(\mathrm{1}+{e}^{−{x}} \right)}\:. \\ $$ Commented by math khazana by abdo…
Question Number 34263 by math khazana by abdo last updated on 03/May/18 $${calculate}\:{I}\:\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{{n}} \right)}\:\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{x}^{{n}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{{n}} \right)}{dx}\:{with}\:{n}\:{integr}\:>\mathrm{0} \\…
Question Number 34258 by math khazana by abdo last updated on 03/May/18 $$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:\forall\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\:\mathrm{1}−\frac{\mathrm{1}}{{x}}\leqslant{lnx}\leqslant\:{x}−\mathrm{1}\right. \\ $$$$\left.\mathrm{2}\right)\:{find}\:\mathrm{2}\:{sequences}\:{u}_{{n}} \:{and}\:{v}_{{n}} \:\:\:/ \\ $$$${u}_{{n}} \leqslant\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{ln}\left(\frac{{k}}{{n}}\right)\leqslant{v}_{{n}} \:\:\:\:\forall{n}\geqslant\mathrm{2} \\ $$…
Question Number 34226 by abdo imad last updated on 03/May/18 $${let}\:{u}_{{n}} =\:\left({n}+\mathrm{1}\right)^{\frac{{n}+\mathrm{1}}{{n}}} \:\:−{n}^{\frac{{n}}{{n}−\mathrm{1}}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} \\ $$ Commented by abdo mathsup 649 cc last…