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 $$\bigtriangledown{f}={grad}\:{f}=\begin{pmatrix}{\frac{\partial{f}}{\partial{x}}}\\{\frac{\partial{f}}{\partial{y}}}\end{pmatrix}…
Question Number 138085 by liberty last updated on 10/Apr/21 $${Given}\:{a}\:{curve}\:{y}\:=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}. \\ $$$${Find}\:{the}\:{equation}\:{of}\:{tangent} \\ $$$${line}\:{with}\:{have}\:{slope}\:{of}\:{tangent} \\ $$$${minimum}\:. \\ $$ Answered by EDWIN88 last updated on…
Question Number 138009 by bobhans last updated on 09/Apr/21 $$\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\sqrt{\mathrm{sec}\:^{\mathrm{3}} \left({x}\right)}\:{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 09/Apr/21 $$\mathcal{E}\:=\:\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\mathrm{sec}\:\left({x}\right)\:\sqrt{\mathrm{sec}\:\left({x}\right)}\:{dx} \\ $$$$=\:\int\:\mathrm{tan}\:\left({x}\right)\mathrm{sec}\:\left({x}\right)\left(\mathrm{sec}\:^{\mathrm{2}}…
Question Number 138004 by benjo_mathlover last updated on 09/Apr/21 $$ \\ $$What is the minimum value of x+y+z, subject to the condition xyz = a³?…