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 $${By}\:{Langrange}\:{multiplier} \\ $$$${f}\left({x},{y},\lambda\right)=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\lambda\left(\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{6}{y}^{\mathrm{2}} −\mathrm{9}\right) \\ $$$$\frac{\partial{f}}{\partial{x}}\:=\:\mathrm{2}{x}+\lambda\left(\mathrm{12}{x}+\mathrm{2}{y}\right)=\mathrm{0}…
Question Number 137597 by bemath last updated on 04/Apr/21 $$ \\ $$Find the minimum value of x^(2) +y^(2) +z^(2) , subject to the condition 2x+3y+5z=30?…
Question Number 72044 by 20190927 last updated on 23/Oct/19 $$\mathrm{y}=\mathrm{ln}\left(\mathrm{3x}^{\mathrm{2}} +\mathrm{x}\right)\:\:\:\mathrm{solve}\:\mathrm{y}^{\left(\mathrm{6}\right)} \left(\mathrm{x}\right) \\ $$ Commented by mathmax by abdo last updated on 24/Oct/19 $${we}\:{have}\:{y}^{'} \left({x}\right)=\frac{\mathrm{6}{x}+\mathrm{1}}{\mathrm{3}{x}^{\mathrm{2}}…
Question Number 137378 by benjo_mathlover last updated on 02/Apr/21 $${Given}\:\underset{\mathrm{0}} {\int}^{\:{x}} {f}\left({t}\right)\:{dt}\:=\:{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\pi{x}\right) \\ $$$${find}\:{f}\left(\mathrm{2}\right). \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\int_{\mathrm{0}}…