Question Number 141368 by bemath last updated on 18/May/21 $${A}\:{closed}\:{cylindrical}\:{can}\:{be}\:{is}\:{to}\:{hold} \\ $$$$\mathrm{1}\:{liters}\:{of}\:{liquid}\:.\:{How}\:{should}\:{we}\: \\ $$$${choose}\:{the}\:{height}\:{and}\:{radius}\: \\ $$$${to}\:{minimize}\:{the}\:{amount}\:{of} \\ $$$${material}\:{needed}\:{to}\:{manufacture} \\ $$$${the}\:{can}\:?\: \\ $$ Answered by TheSupreme…
Question Number 141346 by mnjuly1970 last updated on 17/May/21 Answered by qaz last updated on 17/May/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}−{x}^{\mathrm{2}} }{dx} \\ $$$$=\int_{\mathrm{0}} ^{\infty} \frac{{y}^{\mathrm{2}}…
Question Number 75796 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{let}\:\mathrm{be}\:\mathrm{a},\mathrm{b}\:\mathrm{such}\:\mathrm{as}\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} =\mathrm{ab} \\ $$$$\mathrm{find}\:\:\mathrm{out}\:\mathrm{Z}=\frac{\mathrm{a}^{\mathrm{n}} +\mathrm{b}^{\mathrm{n}} }{\mathrm{a}^{\mathrm{n}} −\mathrm{b}^{\mathrm{n}} }\:\:\mathrm{when}\:\:\mathrm{a}\neq\mathrm{0} \\ $$$$ \\ $$ Answered by mr…
Question Number 75795 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Find}\:\mathrm{out}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{argsh}\left(\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\infty}…
Question Number 141328 by mnjuly1970 last updated on 17/May/21 $$……\:{Evaluate}: \\ $$$$\:\:\:\:\:\mathscr{F}\::=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \zeta\left({n}\right)}{{n}+\mathrm{1}}\:=? \\ $$$$……. \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 141320 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:\:\:……{nice}\:……{calculuus}….. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \frac{\mathscr{A}\:{rctan}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{dxdy}=\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}}}{\mathrm{16}} \\ $$$$…..…
Question Number 75793 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{arctanx}}{\mathrm{x}\sqrt{\mathrm{log2}}}\right)^{\mathrm{2}} \mathrm{dx}=\:\pi \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 141322 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:……{advanced}……..{calculus}……. \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\:\:\xi:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } =\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$ \\ $$ Terms of…
Question Number 75762 by aliesam last updated on 16/Dec/19 $${if}\:\:{y}\:{cos}\left({x}\right)+{x}\:{cos}\left({y}\right)\:=\:\pi \\ $$$$ \\ $$$${find}\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:\:\:,\:{x}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141294 by bemath last updated on 17/May/21 $${Find}\:{max}\:\&\:{min}\:{value}\:{of} \\ $$$$\:{f}\left({x}\right)=\frac{{x}}{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{9}}. \\ $$ Answered by MJS_new last updated on 17/May/21 $$\frac{{df}}{{dx}}=\frac{−{x}^{\mathrm{2}} +\mathrm{9}}{\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{9}\right)^{\mathrm{2}}…