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Category: Differentiation

1-5-4x-2x-2-dx-

Question Number 86092 by ar247 last updated on 27/Mar/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}−\mathrm{4}{x}−\mathrm{2}{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by abdomathmax last updated on 27/Mar/20 $${I}\:=\int\:\:\frac{{dx}}{\:\sqrt{−\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}}}\:\:{we}\:{have} \\ $$$${I}=\int\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}−\mathrm{1}\right)}}=\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}}…

Solve-the-following-equation-dy-dx-2-2y-cot-x-dy-dx-y-2-

Question Number 85513 by niroj last updated on 22/Mar/20 $$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\left(\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{cot}}\:\boldsymbol{\mathrm{x}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:=\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \\ $$ Answered by mr W last updated on 22/Mar/20 $$\frac{{dy}}{{dx}}=−{y}\:\mathrm{cot}\:{x}\pm\sqrt{{y}^{\mathrm{2}} \mathrm{cot}^{\mathrm{2}}…

Given-x-y-real-number-such-that-0-lt-y-x-lt-1-2-Find-minimum-value-of-2y-x-y-3x-x-2y-

Question Number 150963 by EDWIN88 last updated on 17/Aug/21 $${Given}\:{x}\:,{y}\:{real}\:{number}\:{such}\:{that} \\ $$$$\:\mathrm{0}<\frac{{y}}{{x}}<\frac{\mathrm{1}}{\mathrm{2}}.\:{Find}\:{minimum}\:{value} \\ $$$${of}\:\frac{\mathrm{2}{y}}{{x}−{y}}\:+\frac{\mathrm{3}{x}}{{x}+\mathrm{2}{y}}\:.\: \\ $$ Answered by john_santu last updated on 17/Aug/21 $$\:\mathrm{let}\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:\mathrm{t}\:\Rightarrow\mathrm{f}\left(\mathrm{t}\right)=\frac{\mathrm{2t}}{\mathrm{1}−\mathrm{t}}+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{2t}}\: \\…