Question Number 61660 by maxmathsup by imad last updated on 05/Jun/19 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{3}} \right)^{{n}} }\:{dt}\:\:\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{{U}_{{n}+\mathrm{1}} }{{U}_{{n}} } \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{serie}\:\Sigma{ln}\left(\frac{{U}_{{n}+\mathrm{1}} }{{U}_{{n}} }\right)\:\:{and}\:{prove}\:\:{that}\:{lim}_{{n}\rightarrow+\infty}…
Question Number 61657 by maxmathsup by imad last updated on 05/Jun/19 $${U}_{{n}} \:{and}\:{V}_{{n}} \:\:{are}\:{two}\:{sequences}\:\:{verify}\:\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{V}_{{k}} \\ $$$${determine}\:{V}_{{n}} \:\:{interms}\:{of}\:\:{U}_{{k}} \:\:\:\:\:\:\:,\mathrm{0}\leqslant{k}\leqslant{n} \\ $$…
Question Number 127190 by bramlexs22 last updated on 27/Dec/20 $$\:\int\:\frac{\sqrt{{a}}−\sqrt{{x}}}{\mathrm{1}−\sqrt{{ax}}}\:{dx}\:=?\:;\:{a}>\mathrm{0} \\ $$ Answered by Dwaipayan Shikari last updated on 27/Dec/20 $$\Rightarrow{ax}={u}^{\mathrm{2}} \Rightarrow{a}=\mathrm{2}{u}\frac{{du}}{{dx}} \\ $$$$\mathrm{2}\int\frac{\sqrt{{a}}−\frac{{u}}{\:\sqrt{{a}}}}{\mathrm{1}−{u}}.\frac{{u}}{{a}}{du}\:=\:\frac{\mathrm{2}}{\:\sqrt{{a}^{\mathrm{3}} }}\int\frac{{a}−{u}}{\mathrm{1}−{u}}{du}=\frac{\mathrm{2}}{\:\sqrt{{a}^{\mathrm{3}}…
Question Number 61654 by aliesam last updated on 05/Jun/19 $$\int_{\mathrm{0}} ^{\infty} {e}^{−{e}^{{x}} } {ln}\left({x}\right)\:{dx}\:=\:\mathrm{0}.\mathrm{27634} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61652 by maxmathsup by imad last updated on 05/Jun/19 $${solve}\:{inside}\:{C}\:\:{z}^{\mathrm{4}} \:=\frac{\mathrm{1}−{i}}{\mathrm{1}+{i}\sqrt{\mathrm{3}}} \\ $$ Commented by maxmathsup by imad last updated on 06/Jun/19 $${we}\:{have}\:\mid\mathrm{1}−{i}\mid=\sqrt{\mathrm{2}}\:\Rightarrow\mathrm{1}−{i}\:=\sqrt{\mathrm{2}}{e}^{−\frac{{i}\pi}{\mathrm{4}}}…
Question Number 192721 by York12 last updated on 25/May/23 $$ \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} =\mathrm{18} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{26} \\ $$$${and}\:{what}\:{do}\:{you}\:{recommend}\:{to}\:{read}\:{to}\:{deal} \\ $$$${with}\:{such}\:{problems} \\ $$ Answered…
Question Number 127186 by Dwaipayan Shikari last updated on 27/Dec/20 $$\int_{\mathrm{0}} ^{{a}} {e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\sqrt{\pi}}{\mathrm{2}}−\frac{{e}^{−{a}^{\mathrm{2}} } }{\mathrm{2}{a}+\frac{\mathrm{1}}{{a}+\frac{\mathrm{2}}{\mathrm{2}{a}+\frac{\mathrm{3}}{{a}+\frac{\mathrm{4}}{\mathrm{2}{a}+…}}}}}\:\left({Prove}\right) \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 61651 by maxmathsup by imad last updated on 05/Jun/19 $${let}\:{p}\left({x}\right)\:=\left({x}+{i}\sqrt{\mathrm{3}}\right)^{{n}} +\left({x}−{i}\sqrt{\mathrm{3}}\right)^{{n}} \:\:\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{simlify}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){decompose}\:{inside}\:{C}\left[{x}\right]\:\:{p}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {p}\left({x}\right){dx}\: \\…
Question Number 192720 by pascal889 last updated on 25/May/23 Answered by Frix last updated on 25/May/23 $${x}={p}−{q}\wedge{y}={p}+{q} \\ $$$$\Rightarrow \\ $$$$\mathrm{5}{p}^{\mathrm{4}} +\mathrm{6}{p}^{\mathrm{2}} {q}^{\mathrm{2}} +\mathrm{5}{q}^{\mathrm{4}} =\mathrm{109}…
Question Number 127187 by Dwaipayan Shikari last updated on 27/Dec/20 $$\mathrm{1}−\mathrm{5}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{3}} +\mathrm{9}\left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{3}} −\mathrm{13}\left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{3}}{\mathrm{4}}.\frac{\mathrm{5}}{\mathrm{6}}\right)^{\mathrm{3}} +..=\frac{\mathrm{2}}{\pi}\:\left({prove}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 27/Dec/20 Terms…