Question Number 107638 by mathdave last updated on 11/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173164 by SANOGO last updated on 07/Jul/22 Answered by CElcedricjunior last updated on 08/Jul/22 $$\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{M}}\right)=\mathrm{0}−\boldsymbol{\mathrm{a}}\left(\mathrm{1}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} \right)+\boldsymbol{\mathrm{a}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{a}}^{\mathrm{3}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\boldsymbol{\mathrm{a}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{4}} −\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{M}}\:\boldsymbol{\mathrm{inversible}}\:\boldsymbol{\mathrm{if}}…
Question Number 107618 by mathdave last updated on 11/Aug/20 Answered by hgrocks last updated on 11/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107621 by mathdave last updated on 11/Aug/20 Commented by john santu last updated on 12/Aug/20 $$\Gamma\left(\mathrm{2}{x}\right)\:=\:\frac{\mathrm{4}^{{x}} \:\Gamma\left({x}\right)\:\Gamma\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}\sqrt{\pi}}\:.\: \\ $$$${put}\:{x}\:=\:\frac{{n}}{\mathrm{4}} \\ $$$$\Gamma\left(\frac{{n}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{4}^{\frac{{n}}{\mathrm{4}}} \Gamma\left(\frac{{n}}{\mathrm{4}}\right)\Gamma\left(\frac{{n}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}\sqrt{\pi}}\: \\…
Question Number 107617 by mathdave last updated on 11/Aug/20 Answered by Ar Brandon last updated on 11/Aug/20 $$\mathrm{I}=\int\mathrm{sec}^{\mathrm{3}} \mathrm{xtan}^{\mathrm{3}} \mathrm{xdx} \\ $$$$\:\:=\int\mathrm{sec}^{\mathrm{2}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)\mathrm{secxtanxdx} \\…
Question Number 107609 by mathdave last updated on 11/Aug/20 Answered by mr W last updated on 11/Aug/20 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}+\mathrm{4}} \\ $$$$=\underset{{k}=\mathrm{5}} {\overset{{n}+\mathrm{4}} {\sum}}\frac{\mathrm{1}}{{k}} \\…
Question Number 173129 by Gbenga last updated on 07/Jul/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107589 by mathdave last updated on 11/Aug/20 Answered by Ar Brandon last updated on 11/Aug/20 $$\mathcal{I}=\int\left(\frac{\mathrm{x}+\mathrm{6}}{\mathrm{x}+\mathrm{8}}\right)^{\mathrm{6}} \mathrm{dx}=\int\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{x}+\mathrm{8}}\right)^{\mathrm{6}} \mathrm{dx} \\ $$$$\:\:\:=\int\left\{\mathrm{1}−\frac{\mathrm{12}}{\mathrm{x}+\mathrm{8}}+\frac{\mathrm{60}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{2}} }−\frac{\mathrm{160}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{3}} }+\frac{\mathrm{240}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{4}} }−\frac{\mathrm{192}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{5}}…
Question Number 173116 by ali009 last updated on 06/Jul/22 $${let}\:{w}={e}^{{i}\pi/\mathrm{4}} =\left(\mathrm{1}+{i}\right)/\sqrt{\mathrm{2}\:}\:{show}\:{that}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{i}}{erf}\left({wx}\sqrt{\frac{\pi}{\mathrm{2}}}\right)=\int_{\mathrm{0}} ^{{x}} {e}^{−{i}\:{t}^{\mathrm{2}} \:\pi/\mathrm{2}} \:{dt}={c}\left({x}\right)−{is}\left({x}\right) \\ $$ Commented by ali009 last updated on…
Question Number 107586 by Tinku Tara last updated on 11/Aug/20 $$\mathrm{App}\:\mathrm{Updates}:\:\mathrm{v2}.\mathrm{135} \\ $$$$\bullet\:\mathrm{fix}\:\mathrm{for}\:\mathrm{background}\:\mathrm{color}\:\mathrm{problems} \\ $$$$\bullet\:\mathrm{new}\:\mathrm{drawing}\:\mathrm{tools}\:\mathrm{added}\:\mathrm{in} \\ $$$$\:\:\:\mathrm{build}\:\mathrm{and}\:\mathrm{edit}\:\mathrm{menu} \\ $$$$\:\:\:\mathrm{add}\:\mathrm{equality}\:\mathrm{marker}\:\mathrm{to}\:\mathrm{line}\:\mathrm{etc} \\ $$$$\bullet\:\mathrm{A}\:\mathrm{new}\:\mathrm{drawling}\:\mathrm{tool}\:\mathrm{to}\:\mathrm{draw} \\ $$$$\:\:\:\:\mathrm{smooth}\:\mathrm{curves}. \\ $$…