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Question Number 144389 by liberty last updated on 25/Jun/21 $$\:\int\:\left(\mathrm{x}−\mathrm{1}\right)\mathrm{h}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} −\mathrm{sin}\:\mathrm{2x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:+\:\mathrm{c}\: \\ $$$$\Rightarrow\mathrm{h}\:'\left(\mathrm{1}\right)=\:? \\ $$ Answered by mathmax by abdo last updated on 25/Jun/21…
Question Number 144351 by mnjuly1970 last updated on 24/Jun/21 $$ \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:{Evaluate}\:\:\::: \\ $$$$\:\: \\ $$$$\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\left.\:{sin}\:\sqrt[{\:\mathrm{3}\:}]{{x}}\:\right){log}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{{x}}{dx}=? \\ $$$$\:\:\: \\ $$$$ \\…
Question Number 144311 by mnjuly1970 last updated on 24/Jun/21 $$ \\ $$$$\:\:\:\:\:\:……\mathrm{Nice}\:\:\:\:….\:\:\:\:\mathrm{Calculus}…… \\ $$$$\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\Theta\::=\underset{{n}\:=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{4}^{\:{n}} \:{cos}^{\:\mathrm{2}} \:\left(\frac{\:\pi}{\:\mathrm{2}^{\:{n}\:+\:\mathrm{2}} }\:\right)\:\:}\:=? \\ $$$$\:\:\:\:……….…
Question Number 144301 by liberty last updated on 24/Jun/21 Answered by imjagoll last updated on 24/Jun/21 $$\mathrm{we}\:\mathrm{convert}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{2t}+\mathrm{3}\:\mathrm{liters} \\ $$$$\mathrm{per}\:\mathrm{minute}\:\mathrm{to}\:\mathrm{60}\left(\mathrm{2t}+\mathrm{3}\right)=\mathrm{120t}+\mathrm{180} \\ $$$$\mathrm{liters}\:\mathrm{per}\:\mathrm{hours}.\:\mathrm{The}\:\mathrm{total}\:\mathrm{amount} \\ $$$$\mathrm{of}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{time}\:\mathrm{T} \\ $$$$\mathrm{hours}\:\mathrm{past}\:\mathrm{noon}\:\mathrm{is}\:\mathrm{the}\:\mathrm{integral}…
Question Number 13226 by chux last updated on 16/May/17 $$\mathrm{if}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{3axy},\mathrm{find}\:\mathrm{dy}/\mathrm{dx}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{dy}/\mathrm{dx}\: \\ $$$$\mathrm{cannot}\:\mathrm{be}\:\mathrm{equal}\:\mathrm{to}\:-\mathrm{1}\:\mathrm{for}\:\mathrm{finite} \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{except}\:\mathrm{x}=\mathrm{y}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\: \\…
Question Number 144200 by bramlexs22 last updated on 23/Jun/21 $$\mathrm{Find},\:\mathrm{among}\:\mathrm{all}\:\mathrm{right}\:\mathrm{circular} \\ $$$$\mathrm{cylinders}\:\mathrm{of}\:\mathrm{fixed}\:\mathrm{volume}\:\mathrm{V}\: \\ $$$$\mathrm{that}\:\mathrm{one}\:\mathrm{with}\:\mathrm{smallest}\:\mathrm{surface}\:\mathrm{area} \\ $$$$\left(\mathrm{counting}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{faces}\:\right. \\ $$$$\left.\mathrm{at}\:\mathrm{top}\:\mathrm{and}\:\mathrm{bottom}\:\right) \\ $$ Answered by MJS_new last updated…
Question Number 13068 by tawa tawa last updated on 13/May/17 $$\mathrm{If}\:\:\:\mathrm{y}\:=\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}\:\:\:\:\:\mathrm{Find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle} \\ $$ Answered by ajfour last updated on 13/May/17 $$\frac{{dy}}{{dx}}=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+{h}\right)^{\mathrm{1}/\mathrm{3}} −{x}^{\mathrm{1}/\mathrm{3}} }{{h}} \\…
Question Number 78581 by john santu last updated on 18/Jan/20 $$\int\:\frac{\mathrm{2}{x}\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Commented by john santu last updated on 19/Jan/20 $${consider}\: \\ $$$$\frac{\mathrm{2}{x}\:\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}}…
Question Number 424 by 123456 last updated on 25/Jan/15 $${f}\left({x},{y}\right)=\frac{\left({x}+{y}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$$\begin{cases}{\frac{\partial{f}}{\partial{u}}=?}\\{\frac{\partial{f}}{\partial{v}}=?}\end{cases} \\ $$$$\begin{cases}{{x}={uv}}\\{{y}={u}+{v}}\end{cases} \\ $$ Answered by prakash jain last updated…