Question Number 28264 by abdo imad last updated on 22/Jan/18 $${give}\:{the}\:{decomposition}\:{of}\: \\ $$$${F}\left({x}\right)\:\:\:=\:\:\:\:\:\:\frac{\mathrm{1}\:}{\prod_{{k}=\mathrm{1}} ^{{n}} \:\left({x}−{k}^{\mathrm{2}} \right)}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28265 by abdo imad last updated on 22/Jan/18 $$\left.\mathrm{1}\right)\:\:{find}\:{P}\in{R}\left[{x}\right]\:/\:{P}\left({sinx}\right)\:={sin}\left(\mathrm{2}{n}+\mathrm{1}\right){x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\:{and}\:{degP} \\ $$$$\left.\mathrm{3}\right)\:{decompose}\:\:\frac{\mathrm{1}}{{P}}\:\:{and}\:{prove}\:{that} \\ $$$$\frac{\mathrm{2}{n}+\mathrm{1}}{{sin}\left(\mathrm{2}{n}+\mathrm{1}\right){x}}\:=\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{k}} \:{cos}\left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)}{{sinx}−{sin}\:\left(\frac{{k}\pi}{\left.\mathrm{2}{n}+\mathrm{1}\right)}\right)}\:\:. \\ $$ Terms of Service…
Question Number 159332 by 0731619 last updated on 15/Nov/21 Commented by bobhans last updated on 16/Nov/21 $$\left(\mathrm{1}\right)\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{−} } \:\sqrt{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{undefined}\: \\ $$$$\:\:\:\:\:\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\sqrt{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{−}…
Question Number 159325 by mnjuly1970 last updated on 15/Nov/21 $$ \\ $$$$\:\:\:\:\:\:#\:\mathrm{T}{rigonometry}# \\ $$$$\:\:\:\:\:\:\:{solve}\:\left(\:\:\:\mathscr{E}{quation}\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:{sin}\left(\frac{{x}}{\mathrm{2}}\:\right)\:−\:\mathrm{2}{sin}\:\left(\frac{{x}}{\mathrm{3}}\:\right)=\:\mathrm{0}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$ Commented…
Question Number 159300 by saly last updated on 15/Nov/21 Answered by Derrick last updated on 15/Nov/21 $${preve} \\ $$$$\left.{a}\right){montrons}\:{par}\:{double}\:{inclusion} \\ $$$${soit}\:{x} \\ $$$${x}\in{f}^{−\mathrm{1}} \:\left({A}\cup{B}\right)\Leftrightarrow{f}\left({x}\right)\in\left({A}\cup{B}\right) \\…
Question Number 28219 by math solver last updated on 22/Jan/18 Commented by mrW2 last updated on 22/Jan/18 $${z}={x}+{iy} \\ $$$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{2}{y}\right)^{\mathrm{2}} =\left({x}−\mathrm{1}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}}…
Question Number 159292 by HongKing last updated on 15/Nov/21 $$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{x}\:\mathrm{arctan}\left(\mathrm{x}\right)}{\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}\:\mathrm{dx} \\ $$$$ \\ $$ Answered by mindispower last updated on 15/Nov/21 $$=\int_{\mathrm{0}}…
Question Number 28211 by ajfour last updated on 22/Jan/18 Commented by math solver last updated on 22/Jan/18 $${thank}\:{you}\:{sir}! \\ $$ Commented by math solver last…
Question Number 159281 by HongKing last updated on 14/Nov/21 Commented by MJS_new last updated on 14/Nov/21 $${x}=−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{how}? \\ $$$$\mathrm{obviously}\:{x}<\mathrm{0}\:\mathrm{because}\:\mathrm{otherwise}\:\mathrm{lhs}\:>\mathrm{0} \\ $$$$\mathrm{but}\:\mathrm{with}\:{x}=−\mathrm{1}\:\mathrm{lhs}\:<\mathrm{0}\:\Rightarrow\:−\mathrm{1}<{x}<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{I}\:\mathrm{tried}\:{x}=−\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\mathrm{lhs}\:<\mathrm{0}\:\Rightarrow\:−\frac{\mathrm{1}}{\mathrm{2}}<{x}<\mathrm{0}…
Question Number 93742 by I want to learn more last updated on 14/May/20 $$\mathrm{No}\:\mathrm{my}\:\mathrm{post}\:\mathrm{option}\:\mathrm{again}?? \\ $$$$\mathrm{at}\:\mathrm{Tinkutara}. \\ $$$$\mathrm{because}\:\mathrm{i}\:\mathrm{cannot}\:\mathrm{find}\:\mathrm{my}\:\mathrm{post}\:\mathrm{options}\:\mathrm{again} \\ $$ Commented by Ar Brandon last…