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Category: Differentiation

Q1-A-balloon-in-the-shape-of-cone-surrmo-surmounted-by-hemispherical-top-the-daimeter-of-balloon-is-equal-to-hieght-of-cone-find-the-rate-of-change-of-volume-of-the

Question Number 7265 by 2402@gmail.com last updated on 20/Aug/16 $${Q}\mathrm{1}.\:{A}\:{balloon}\:{in}\:{the}\:{shape}\:{of}\:{cone}\:{surrmo} \\ $$$$\:\:\:\:\:\:\:\:\:\:{surmounted}\:{by}\:{hemispherical} \\ $$$$\:\:\:\:\:\:\:\:\:{top}\:.\:{the}\:{daimeter}\:{of}\:{balloon}\:{is} \\ $$$$\:\:\:\:\:\:\:{equal}\:{to}\:{hieght}\:{of}\:{cone}\:.\:{find}\:{the} \\ $$$$\:\:\:\:\:{rate}\:{of}\:{change}\:{of}\:{volume}\:{of}\:{the} \\ $$$$\:\:\:{balloone}\:{with}\:{respect}\:{to}\:{its}\:{total} \\ $$$$\:\:\:\:{height}\:\:{h}\:. \\ $$ Commented…

Question-72724

Question Number 72724 by rajesh4661kumar@gmail.com last updated on 01/Nov/19 Commented by kaivan.ahmadi last updated on 01/Nov/19 $$\frac{\pi}{\mathrm{2}}<{x}_{\mathrm{1}} <{x}_{\mathrm{2}} <\pi\Rightarrow\mathrm{0}<\mid{cosx}_{\mathrm{2}} \mid<\mid{cosx}_{\mathrm{1}} \mid<\mathrm{1}\Rightarrow \\ $$$${log}\mid{cosx}_{\mathrm{2}} \mid<{log}\mid{cosx}_{\mathrm{1}} \mid…

mathematical-analysis-if-0-1-arctan-x-ln-1-x-2-x-2-dx-1-48-api-2-bpiln-2-c-ln-2-2-then-a-2-b-c-1-2-

Question Number 138171 by mnjuly1970 last updated on 11/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:…….{mathematical}….{analysis}……. \\ $$$$\:\:\:\:\:{if}\::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{48}}\left({a}\pi^{\mathrm{2}} −{b}\pi{ln}\left(\mathrm{2}\right)+{c}\:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:……{then}\:\:….\:{a}^{\mathrm{2}} +\left({b}−{c}+\mathrm{1}\right)^{\mathrm{2}} =??? \\…

advanced-calculus-find-the-value-of-n-1-1-n-H-2n-n-

Question Number 138145 by mnjuly1970 last updated on 10/Apr/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:………..{advanced}\:…\:…\:…\:{calculus}……… \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Theta=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \mathrm{H}_{\mathrm{2}{n}} }{{n}}=??? \\ $$ Answered by Dwaipayan…

f-x-y-ax-2-by-2-How-do-you-find-where-the-gradient-is-zero-for-multivariable-funtions-

Question Number 7040 by FilupSmith last updated on 07/Aug/16 $${f}\left({x},{y}\right)={ax}^{\mathrm{2}} +{by}^{\mathrm{2}} \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{where}\:\mathrm{the}\:\mathrm{gradient} \\ $$$$\mathrm{is}\:\mathrm{zero}\:\mathrm{for}\:\mathrm{multivariable}\:\mathrm{funtions}? \\ $$ Commented by Yozzii last updated on 07/Aug/16 $$\bigtriangledown{f}={grad}\:{f}=\begin{pmatrix}{\frac{\partial{f}}{\partial{x}}}\\{\frac{\partial{f}}{\partial{y}}}\end{pmatrix}…