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Category: Differentiation

A-closed-cylindrical-can-be-is-to-hold-1-liters-of-liquid-How-should-we-choose-the-height-and-radius-to-minimize-the-amount-of-material-needed-to-manufacture-the-can-

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…

let-be-a-b-such-as-a-2-b-2-ab-find-out-Z-a-n-b-n-a-n-b-n-when-a-0-

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…

nice-calculuus-prove-that-0-0-A-rctan-x-2-y-2-x-4-y-4-dxdy-pi-2-2-16-

Question Number 141320 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:\:\:……{nice}\:……{calculuus}….. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \frac{\mathscr{A}\:{rctan}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{dxdy}=\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}}}{\mathrm{16}} \\ $$$$…..…