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if-7x-pi-2-cosxsin2xtan3x-cot4xcos5xsin6x-

Question Number 204618 by es last updated on 23/Feb/24 $${if}\:\:\mathrm{7}{x}=\frac{\pi}{\mathrm{2}}\rightarrow\frac{{cosxsin}\mathrm{2}{xtan}\mathrm{3}{x}}{{cot}\mathrm{4}{xcos}\mathrm{5}{xsin}\mathrm{6}{x}}=? \\ $$ Answered by A5T last updated on 23/Feb/24 $$\frac{\frac{{cos}\left({x}\right){sin}\left(\mathrm{2}{x}\right){sin}\left(\mathrm{3}{x}\right)}{{cos}\left(\mathrm{3}{x}\right)}}{\frac{{cos}\left(\mathrm{4}{x}\right){cos}\left(\mathrm{5}{x}\right){sin}\left(\mathrm{6}{x}\right)}{{sin}\left(\mathrm{4}{x}\right)}} \\ $$$$=\frac{{sin}\left(\mathrm{4}{x}\right){cos}\left({x}\right){sin}\left(\mathrm{2}{x}\right){sin}\left(\mathrm{3}{x}\right)}{{cos}\left(\mathrm{3}{x}\right){cos}\left(\mathrm{4}{x}\right){cos}\left(\mathrm{5}{x}\right){sin}\left(\mathrm{6}{x}\right)}=\mathrm{1} \\ $$$$\left[{since}\:{sin}\left(\mathrm{4}{x}\right)={cos}\left(\mathrm{3}{x}\right);{cos}\left({x}\right)={sin}\left(\mathrm{6}{x}\right);\right. \\…

exercice-prouver-0-0-x-sin-x-2-dxdy-prof-cedric-junior-

Question Number 204615 by lepuissantcedricjunior last updated on 26/Feb/24 $$\:\:\:\:\:\:\:\:\frac{\boldsymbol{\mathrm{exercice}}\:}{} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{prouver}}\:\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \boldsymbol{{sin}}\left(\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\pi}}\right)\boldsymbol{{d}\mathrm{x}{d}\mathrm{y}}=\boldsymbol{\pi} \\ $$$$\: \\ $$$$\:\:……………\boldsymbol{{prof}}\:\boldsymbol{{cedric}}\:\boldsymbol{{junior}}……….. \\ $$$$ \\ $$…

x-x-2-1-3-dx-

Question Number 204598 by SEKRET last updated on 22/Feb/24 $$\:\:\:\:\:\:\:\:\int\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{dx}} \\ $$$$ \\ $$ Commented by Frix last updated on 23/Feb/24 $${t}=\mathrm{sin}^{−\mathrm{1}} \:\sqrt{{x}}\:\Rightarrow \\…

f-x-x-3-16x-2-57x-1-f-a-0-f-b-0-f-c-0-a-1-5-b-1-5-c-1-5-

Question Number 204595 by SEKRET last updated on 22/Feb/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:=\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:−\:\mathrm{16}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{57}\boldsymbol{\mathrm{x}}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{a}}\right)=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{b}}\right)=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{c}}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{a}}}\:+\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{b}}\:}\:+\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{c}}\:}\:=\:? \\ $$ Answered by mr W last updated on…

How-Can-we-prove-h-J-h-z-1-

Question Number 204468 by MathedUp last updated on 18/Feb/24 $$\mathrm{How}\:\mathrm{Can}\:\mathrm{we}\:\mathrm{prove}\:\underset{{h}=−\infty} {\overset{\infty} {\sum}}\:{J}_{{h}} \left({z}\right)=\mathrm{1} \\ $$ Answered by Peace last updated on 19/Feb/24 $${J}_{{n}−\mathrm{1}} \left({x}\right)+{j}_{{n}+\mathrm{1}} \left({x}\right)=\frac{\mathrm{2}{n}}{{x}}{j}_{{n}}…