Question Number 3996 by Rasheed Soomro last updated on 26/Dec/15 $${I}\:{want}\:{to}\:{make}\:{cyllinders}\:{of}\:\boldsymbol{{maximum}} \\ $$$$\boldsymbol{{volume}}\:\boldsymbol{\mathrm{V}}_{\boldsymbol{\mathrm{max}}} \:{with}\:{minimum}\:\boldsymbol{{surface}}\:\boldsymbol{{area}}\: \\ $$$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{min}}} \:,{because}\:{they}\:{are}\:{more}\:{profitable}\:{for}\:{me}. \\ $$$${I}\:{need}\:{the}\:{help}\:{of}\:{mathematicians}\:{of}\:{this} \\ $$$${forum}. \\ $$$$ \\ $$…
Question Number 135065 by liberty last updated on 10/Mar/21 $$\mathrm{cosec}\:^{\mathrm{2}} \mathrm{68}°\:+\mathrm{sec}\:^{\mathrm{2}} \mathrm{56}°\:−\mathrm{cot}\:^{\mathrm{2}} \mathrm{34}°\:−\mathrm{tan}\:^{\mathrm{2}} \mathrm{22}°\:=? \\ $$ Commented by som(math1967) last updated on 10/Mar/21 $$\mathrm{2} \\…
Question Number 3994 by Filup last updated on 26/Dec/15 $$\mathcal{A}\mathrm{re}\:\mathrm{there}\:\mathrm{more}\:\:\mathcal{T}{rancendental} \\ $$$${or}\:\mathcal{N}{on}-\mathcal{T}{rancendental}\:{numbers}? \\ $$$$ \\ $$$$\mathcal{NOTE}: \\ $$$$\mathcal{T}{rancendentals}\:{are}\:{numbers}\:{that} \\ $$$${cannot}\:{be}\:{written}\:{algerbraically}. \\ $$$$ \\ $$$${e}.{g}.\:{x}^{\mathrm{2}} =\mathrm{2}…
Question Number 135061 by liberty last updated on 09/Mar/21 $$ \\ $$How can I solve the differential equation (1+x^2)^2y′′+2x(1+x^2)y′+4y=0 Answered by EDWIN88 last updated on 10/Mar/21…
Question Number 135060 by liberty last updated on 09/Mar/21
Question Number 135062 by liberty last updated on 09/Mar/21 $$\mathrm{Let}\:\mathrm{f}\left(\mathrm{0}\right)\:=\:\mathrm{a}\:;\:\mathrm{f}\left(\mathrm{3}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{f}\:'\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}^{\mathrm{4}} } \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\int_{\mathrm{0}} ^{\:\mathrm{3}} \mathrm{x}^{\mathrm{2}} \:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$ Answered by john_santu last updated on 10/Mar/21…
Question Number 3988 by Filup last updated on 26/Dec/15 $${S}=\int_{−\infty} ^{\:\mathrm{0}} \left[\mathrm{sin}\left({e}^{{x}} \right)\:\mathrm{cos}\left({e}^{−{x}} \right)\right]{dx} \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\:\:\mathrm{Solve}\:{S} \\ $$$$ \\ $$$$\mathrm{Also},\:\mathrm{Does}: \\ $$$$\left(\mathrm{2}\right)\:\:\:\int_{\mathrm{0}} ^{\:\infty}…
Question Number 135055 by mnjuly1970 last updated on 09/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:….{dilogarithm}\:\:\:{integral}…. \\ $$$$\:\:\:\:\:\:\:\:\:{calculate}::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}=? \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 135054 by rexford last updated on 09/Mar/21 Commented by mr W last updated on 10/Mar/21 $${there}\:{are}\:{three}\:{possible}\:{answers}: \\ $$$${in}\:{plane}:\:\mid{a}\mid=\frac{\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$$${in}\:{space}:\:\mid{a}\mid=\mathrm{1}\:{or}\:\sqrt{\mathrm{3}} \\ $$ Commented…
Question Number 3974 by Yozzii last updated on 26/Dec/15 $${Define}\:{the}\:{sequence}\:\left\{{a}_{{n}} \right\}\:{by}\:{the} \\ $$$${recursive}\:{formula}\: \\ $$$$\:\:\:{a}_{{n}+\mathrm{1}} ={ca}_{{n}} −{nr}^{{n}−\mathrm{1}} \:\:\:\left({n}\in\mathbb{Z},{n}\geqslant\mathrm{1}\right) \\ $$$${with}\:{a}_{\mathrm{1}} ={h}\:{and}\:{c},{r},{h}\in\mathbb{C},\:{c},{r}\neq\mathrm{0}. \\ $$$${Find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\…