Question Number 139878 by bramlexs22 last updated on 02/May/21 $$\:\:\:\:\:\:\:\mathrm{I}\left(\alpha\right)\:=\:\underset{\alpha} {\overset{\alpha^{\mathrm{2}} } {\int}}\:\frac{\mathrm{sin}\:\alpha\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{dI}\left(\alpha\right)}{\mathrm{d}\alpha}\:=? \\ $$ Answered by EDWIN88 last updated on 02/May/21 $$\:\:\:\:\:\frac{\mathrm{dI}}{\mathrm{d}\alpha}\:=\:\underset{\alpha}…
Question Number 139851 by mnjuly1970 last updated on 01/May/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:…… \\ $$$$\:\:\:\:\:\:\Phi=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)}{\:\sqrt{{x}}}{dx}=\mathrm{4}\:{ln}\left(\frac{{e}}{\mathrm{2}}\right)\:…\checkmark \\ $$ Answered by mindispower last updated on 01/May/21…
Question Number 74235 by aliesam last updated on 20/Nov/19 Answered by Joel578 last updated on 20/Nov/19 $$\mid{x}\mid\:=\:\sqrt{{x}^{\mathrm{2}} } \\ $$$${f}\left({x}\right)\:=\:\sqrt{\left({x}^{\mathrm{2}} \:−\:\mathrm{3}\right)^{\mathrm{2}} } \\ $$$${f}\:'\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\left({x}^{\mathrm{2}} \:−\:\mathrm{3}\right)^{\mathrm{2}}…
Question Number 139694 by mnjuly1970 last updated on 30/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8488 by Basant007 last updated on 12/Oct/16 $${find}\:{y}_{{n}} \:{if}\:{y}=\mathrm{cos}\:\mathrm{2}{x} \\ $$ Commented by FilupSmith last updated on 13/Oct/16 $${y}_{{n}} =\frac{{d}^{{n}} {y}}{{dx}^{{n}} } \\…
Question Number 139555 by snipers237 last updated on 28/Apr/21 $$\:\:\underset{{i}=\mathrm{0}} {\overset{\mathrm{5}} {\prod}}\left(\mathrm{1}−{cotan}\left(\mathrm{20}+{i}\right)\right)\:\:\overset{?} {=}\:\mathrm{8} \\ $$ Answered by mr W last updated on 28/Apr/21 $$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{20}°}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{25}°}\right) \\…
Question Number 139479 by mnjuly1970 last updated on 27/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:….\bigstar\bigstar\bigstar…..{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\: :=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{{sin}\left({n}\right)}{{n}}\right)^{\mathrm{3}} =?\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari last…
Question Number 139457 by mnjuly1970 last updated on 27/Apr/21 $$\:_{} \:\:\: \\ $$$$\:\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}\right)!}\:=\frac{{e}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}\sqrt{{e}}}\:{cos}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right) \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…
Question Number 139404 by mnjuly1970 last updated on 26/Apr/21 $$\:\:\:\:\: \\ $$$$\:\:\:#\:{Question}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{proof}\:::\:\underset{{n}=−\infty} {\overset{\:\infty} {\sum}}\left(\:\frac{{sin}\left({n}\right)}{{n}}\:\right)^{\mathrm{2}} =\pi \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…….\:{nice}\:.{calculus}\:……\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 139323 by snipers237 last updated on 25/Apr/21 $$\:{Let}\:{f}\:{define}\:{such}\:{as}\:\:{f}\left(\mathrm{1}\right)=\mathrm{1},{f}\left(\mathrm{3}\right)=\mathrm{3} \\ $$$$\forall\:{n}\geqslant\mathrm{2}\:\:,\:{f}\left(\mathrm{2}{n}\right)={f}\left({n}\right)\: \\ $$$${f}\left(\mathrm{4}{n}+\mathrm{1}\right)=\mathrm{2}{f}\left(\mathrm{2}{n}+\mathrm{1}\right)−{f}\left({n}\right) \\ $$$${f}\left(\mathrm{4}{n}+\mathrm{3}\right)=\mathrm{3}{f}\left(\mathrm{2}{n}+\mathrm{1}\right)−\mathrm{2}{f}\left({n}\right) \\ $$$$ \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\forall\:{n}\:,\:{f}\left({n}\right)\:{is}\:{odd} \\ $$$$\left.\mathrm{2}\right){Prove}\:{that}\:{if}\:\:\:{f}\left({a}_{{n}} \right)={a}_{{n}} \:, \\…