Question Number 127974 by Dwaipayan Shikari last updated on 03/Jan/21 $$\overset{\bullet\bullet} {\theta}+\frac{{g}}{{l}}{sin}\theta=\mathrm{0} \\ $$$${Exact}\:{form}\:\left({May}\:{include}\:{elliptic}\:{integral}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 03/Jan/21 $${My}\:{try}…
Question Number 127970 by Agnibhoo last updated on 03/Jan/21 $$\mathrm{You}\:\mathrm{have}\:\mathrm{given}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:{N}.\: \\ $$$$\mathrm{Calculate}\: \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \frac{{e}^{\mathrm{2}\pi{x}^{\mathrm{2}} } \:−\:\mathrm{1}}{{e}^{\mathrm{2}\pi{x}^{\mathrm{2}} } \:+\:\mathrm{1}}\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{{x}}{{N}^{\mathrm{2}} \:−\:{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Answered…
Question Number 62413 by mathmax by abdo last updated on 20/Jun/19 $${calculate}\:\:{W}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx}\:\:\:\left(\:{n}\:{from}\:{N}\right)\:{and}\:{J}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{{n}} {xdx} \\ $$ Terms of Service…
Question Number 62410 by mathmax by abdo last updated on 20/Jun/19 $$\:\:{prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}} {ln}\left({t}\right)\:{dt}\:=−\gamma\:\:\:\:\:\:\:\left(\:\:\gamma\:{is}\:{the}\:{constant}\:{of}\:{euler}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127933 by AgnibhoMukhopadhyay last updated on 03/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}\:−\:\mathrm{3}}\:+\:\frac{\mathrm{1}}{{x}\:+\:\mathrm{4}}} \\ $$$$ \\ $$$$\mathrm{If}\:{x}\:>\:\mathrm{0}\:\mathrm{and}\:{x}\:\neq\:\mathrm{3},\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\:\: \\ $$$$\mathrm{following}\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{expresion}\:\mathrm{above}? \\ $$$$\mathrm{A}.\:\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$$$\mathrm{B}.\:\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{12}\: \\ $$$$\mathrm{C}.\:\:\frac{{x}^{\mathrm{2}}…
Question Number 62395 by Cypher1207 last updated on 20/Jun/19 $$\mathrm{The}\:\mathrm{Most}\:\mathrm{Beautiful}\:\mathrm{Equation} \\ $$$$\mathrm{for}\:\mathrm{me}\:\mathrm{is}: \\ $$$$\mathrm{e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{INCREDIBLE}! \\ $$$$#\mathrm{Euler}'\mathrm{sIdentity} \\ $$ Commented by JDamian last…
Question Number 62341 by Tawa1 last updated on 20/Jun/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{root}\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\mathrm{x}^{\mathrm{8}} \:−\:\mathrm{x}^{\mathrm{7}} \:+\:\mathrm{2x}^{\mathrm{6}} \:−\:\mathrm{2x}^{\mathrm{5}} \:+\:\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\frac{\mathrm{5}}{\mathrm{2}}\:\:=\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{has} \\ $$ Commented by Kunal12588 last…
Question Number 127876 by Ar Brandon last updated on 02/Jan/21 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{defined}\:\mathrm{by}:\:\mathrm{0}<\mathrm{u}_{\mathrm{0}} <\mathrm{1}\:\mathrm{and}\:\forall\mathrm{n}\in\mathbb{N},\:\mathrm{u}_{\mathrm{n}+\mathrm{1}} =\mathrm{u}_{\mathrm{n}} −\mathrm{u}_{\mathrm{n}} ^{\mathrm{2}} . \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{u}_{\mathrm{n}} \right)\:\mathrm{converges}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{its}\:\mathrm{limit}\:? \\ $$$$\mathrm{2}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series}\:\mathrm{with}\:\mathrm{general}\:\mathrm{term}\:\mathrm{u}_{\mathrm{n}} ^{\mathrm{2}} \:\mathrm{converges}. \\ $$$$\mathrm{3}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series}\:\mathrm{with}\:\mathrm{general}\:\mathrm{terms}\:\mathrm{ln}\left(\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}}…
Question Number 127859 by AgnibhoMukhopadhyay last updated on 02/Jan/21 Answered by liberty last updated on 03/Jan/21 $$\:\frac{\mathrm{3}−\mathrm{5i}}{\mathrm{8}+\mathrm{2i}}\:×\:\frac{\mathrm{8}−\mathrm{2i}}{\mathrm{8}−\mathrm{2i}}\:=\:\frac{\mathrm{24}−\mathrm{46i}−\mathrm{10}}{\mathrm{64}+\mathrm{4}}=\frac{\mathrm{14}−\mathrm{46i}}{\mathrm{68}} \\ $$$$\:=\:\frac{\mathrm{7}}{\mathrm{34}}−\frac{\mathrm{23i}}{\mathrm{34}} \\ $$ Terms of Service Privacy…
Question Number 62288 by 0987654321 last updated on 19/Jun/19 $${M}_{{TP}} ={Q}\frac{{D}}{{Z}}\:×\:{f}_{} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com