Question Number 48169 by Abdo msup. last updated on 20/Nov/18 $${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({nx}^{\mathrm{2}} \right){dx}\:{and}\:{v}_{{n}} =\int_{\mathrm{0}} ^{\infty} {sin}\left({nx}^{\mathrm{2}} \right){dx}\:{with}\:{n}\:>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{u}_{{n}} {and}\:{v}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{nsture}\:{of}\:\Sigma\left({u}_{{n}} +\mathrm{2}{v}_{{n}}…
Question Number 113632 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\frac{\mathrm{1}}{\mathrm{n}}} ^{\mathrm{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{2}} }\right)\mathrm{arctan}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{t}}\right)\mathrm{dt} \\ $$$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$ Terms of Service Privacy…
Question Number 48068 by maxmathsup by imad last updated on 18/Nov/18 $${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\mathrm{1}+{t}^{{n}} } \\ $$$${find}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} \:\:\:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{n}^{\mathrm{2}} }\:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{n}^{\mathrm{3}} } \\ $$…
Question Number 48065 by maxmathsup by imad last updated on 18/Nov/18 $$\left.{let}\:{f}\:\:\:\::\:\:\right]\mathrm{0},\mathrm{1}\left[\:\:{contnue}\:{integrable}\:\:{u}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} {f}\left({x}\right){dx}\right. \\ $$$${prove}\:{that}\:\Sigma\:{u}_{{n}} \:{cnverge}\:{and}\:{find}\:{its}\:{sum} \\ $$$$ \\ $$ Commented…
Question Number 113549 by mathmax by abdo last updated on 13/Sep/20 $$\mathrm{let}\:\mathrm{A}\:\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\frac{\mathrm{1}}{\mathrm{n}}}\\{\frac{\mathrm{1}}{\mathrm{n}}\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\:\mathrm{A}^{\mathrm{m}} \:\:\:\:\:\left(\mathrm{m}\:\:\mathrm{integr}\:\mathrm{natural}\right) \\ $$$$\left.\mathrm{3}\right)\:\mathrm{coclude}\:\mathrm{A}^{\mathrm{n}} \:\:\:\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{calculate}\:\mathrm{e}^{\mathrm{A}} \:\mathrm{and}\:\mathrm{e}^{−\mathrm{A}} \\…
Question Number 48009 by maxmathsup by imad last updated on 18/Nov/18 $${let}\:\:\:{f}_{{n}} \left({t}\right)={t}^{{n}−\mathrm{1}} {sin}\left({n}\theta\right)\:{with}\:{t}\:{from}\left[\mathrm{0},\mathrm{1}\left[\:{and}\:\:\theta\:{from}\:\left[\mathrm{0},\pi\left[\right.\right.\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{uniform}\:{convergence}\:{of}\:\Sigma\:{f}_{{n}} \left({t}\right)\:{on}\:\left[\mathrm{0},\mathrm{1}\left[\right.\right. \\ $$$$\left.\mathrm{2}\right)\:{let}\:{S}\left({t}\right)=\Sigma\:{f}_{{n}} \left({t}\right)\:\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {S}\left({t}\right){dt}. \\ $$ Terms…
Question Number 47857 by maxmathsup by imad last updated on 15/Nov/18 $${let}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right)\:{and}\:{B}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{cos}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}_{{n}} \:{and}\:{B}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{A}_{{n}}…
Question Number 178635 by infinityaction last updated on 19/Oct/22 $$\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\:\mathrm{log}_{\mathrm{x}^{\mathrm{2}\:\:\:} } \left(\frac{\mathrm{x}}{\mid\mathrm{x}\mid}−\mathrm{x}\right)\geqslant\mathrm{0} \\ $$ Commented by Frix last updated on 19/Oct/22 $${x}\leqslant−\mathrm{2}\vee\mathrm{0}<{x}<\mathrm{1} \\ $$ Commented…
Question Number 178624 by infinityaction last updated on 19/Oct/22 $$\:\:\:\:\:\:\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\mathrm{f}}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\:\mathbb{R}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{by}} \\ $$$$\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:=\:\:\frac{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)^{\mathrm{3}} +\left(\mathrm{1}−\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)^{\mathrm{3}} }{\mathrm{8}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}\:\:\:\boldsymbol{\mathrm{then}} \\ $$$$\:\:\boldsymbol{\mathrm{max}}\left\{\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right):\:\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{1}\right]\right\}−\boldsymbol{\mathrm{min}}\left\{\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right):\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\mathrm{1}\right]\right\} \\ $$$$\mathrm{is} \\ $$ Answered by a.lgnaoui…
Question Number 112681 by bemath last updated on 09/Sep/20 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\left(\mathrm{f}\left(\mathrm{3x}\right)\right)^{\mathrm{2}} \:=\:\left(\mathrm{f}\left(\mathrm{2x}\right)\right)^{\mathrm{2}} +\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} \\ $$ Answered by bobhans last updated on 09/Sep/20 $$\:\left(\blacklozenge\right)\:\left(\mathrm{f}\left(\mathrm{3x}\right)\right)^{\mathrm{2}} \:=\:\left(\mathrm{f}\left(\mathrm{2x}\right)\right)^{\mathrm{2}}…