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 $$\mathcal{E}\:=\:\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\mathrm{sec}\:\left({x}\right)\:\sqrt{\mathrm{sec}\:\left({x}\right)}\:{dx} \\ $$$$=\:\int\:\mathrm{tan}\:\left({x}\right)\mathrm{sec}\:\left({x}\right)\left(\mathrm{sec}\:^{\mathrm{2}}…
Question Number 138004 by benjo_mathlover last updated on 09/Apr/21 $$ \\ $$What is the minimum value of x+y+z, subject to the condition xyz = a³?…
Question Number 72250 by aliesam last updated on 26/Oct/19 $${f}\left({x}\right)=\left({ax}+{b}\right){sin}\left({x}\right)+\left({cx}+{d}\right){cos}\left({x}\right) \\ $$$${and}\:\:\:\frac{{dy}}{{dx}}={xcos}\left({x}\right) \\ $$$${find}\:\:{a}\:,\:{b}\:,\:{c}\:,\:{d} \\ $$$$ \\ $$$$ \\ $$ Commented by kaivan.ahmadi last updated…
Question Number 137741 by bemath last updated on 06/Apr/21 $$ \\ $$How do I use the Lagrange multiplier method to find the maximum of the…
Question Number 137743 by bemath last updated on 06/Apr/21 $$ \\ $$ find the max and min of f(x,y)=81x^2+y^2, subject 4x^2+y^2=9 Answered by EDWIN88 last updated…
Question Number 137650 by bemath last updated on 05/Apr/21 Answered by bemath last updated on 05/Apr/21 $${By}\:{Langrange}\:{multiplier} \\ $$$${f}\left({x},{y},\lambda\right)=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\lambda\left(\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{6}{y}^{\mathrm{2}} −\mathrm{9}\right) \\ $$$$\frac{\partial{f}}{\partial{x}}\:=\:\mathrm{2}{x}+\lambda\left(\mathrm{12}{x}+\mathrm{2}{y}\right)=\mathrm{0}…
Question Number 137597 by bemath last updated on 04/Apr/21 $$ \\ $$Find the minimum value of x^(2) +y^(2) +z^(2) , subject to the condition 2x+3y+5z=30?…