Question Number 138348 by EnterUsername last updated on 12/Apr/21 Commented by EnterUsername last updated on 12/Apr/21 Image courtesy of Anna Lachowska. Terms of Service Privacy…
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 Number 7245 by 2402@gmail.com last updated on 18/Aug/16 $${Q}\mathrm{1}.{if}\:{y}^{\mathrm{1}/{n}} +{y}^{−\mathrm{1}/{n}} \:=\mathrm{2}\:{find}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:. \\ $$$$ \\ $$$$ \\ $$ Commented by Yozzia last updated…
Question Number 138278 by 676597498 last updated on 11/Apr/21 Answered by TheSupreme last updated on 12/Apr/21 $$ \\ $$$$\mathrm{6}{x}=\mathrm{4}\left({mod}\mathrm{5}\right) \\ $$$$\mathrm{6}{x}=\mathrm{2}\left({mod}\mathrm{7}\right) \\ $$$$ \\ $$$$\mathrm{5}{y}_{\mathrm{2}}…
Question Number 72724 by rajesh4661kumar@gmail.com last updated on 01/Nov/19 Commented by kaivan.ahmadi last updated on 01/Nov/19 $$\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 \\ $$$${log}\mid{cosx}_{\mathrm{2}} \mid<{log}\mid{cosx}_{\mathrm{1}} \mid…
Question Number 138209 by 676597498 last updated on 11/Apr/21 $${I}_{{n}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}} \sqrt{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$${find}\:{reduction}\:{formula} \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 138171 by mnjuly1970 last updated on 11/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:…….{mathematical}….{analysis}……. \\ $$$$\:\:\:\:\:{if}\::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{48}}\left({a}\pi^{\mathrm{2}} −{b}\pi{ln}\left(\mathrm{2}\right)+{c}\:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:……{then}\:\:….\:{a}^{\mathrm{2}} +\left({b}−{c}+\mathrm{1}\right)^{\mathrm{2}} =??? \\…
Question Number 138145 by mnjuly1970 last updated on 10/Apr/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:………..{advanced}\:…\:…\:…\:{calculus}……… \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Theta=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \mathrm{H}_{\mathrm{2}{n}} }{{n}}=??? \\ $$ Answered by Dwaipayan…
Question Number 138112 by 676597498 last updated on 10/Apr/21 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left({sin}^{\mathrm{2}{k}} \left({x}\right){dx}\right)=\frac{\left(\mathrm{2}{k}\right)!\mathrm{2}^{−\mathrm{2}{k}−\mathrm{1}} }{\left({k}!\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated…
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}…