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Category: Differentiation

Given-x-y-R-x-y-0-Find-the-maximum-and-minimum-value-of-xy-4y-2-x-2-4y-2-

Question Number 132753 by liberty last updated on 16/Feb/21 $$\mathrm{Given}\:\mathrm{x},\mathrm{y}\:\in\mathbb{R}\:,\:\mathrm{x},\mathrm{y}\neq\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{xy}−\mathrm{4y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{4y}^{\mathrm{2}} }\: \\ $$ Commented by mr W last updated…

Question-132762

Question Number 132762 by liberty last updated on 16/Feb/21 Answered by EDWIN88 last updated on 16/Feb/21 $$\Rightarrow\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{9}\:\Rightarrow\mathrm{x}^{\mathrm{2}} =\mathrm{9}−\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{Volume}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\mathrm{x}^{\mathrm{2}} \left(\mathrm{3}+\mathrm{y}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\left(\mathrm{9}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{3}+\mathrm{y}\right) \\…

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Question Number 1676 by hhhggvghhh last updated on 31/Aug/15 $$\boldsymbol{{hhjghhjjgkggjggigfhpppkknbgjffffg}} \\ $$$$\boldsymbol{{biuggjnggtbnkoyfhjiuhbhuklphh}} \\ $$$$\boldsymbol{{jinbh}}\mathrm{678656}\boldsymbol{{kkiohhuggjngffjkkdooxk}} \\ $$$$\boldsymbol{{ikhhkjhv}}\mathrm{2}\left[\mathrm{65}\sqrt{\sqrt{\mathrm{58}\:\mathrm{889}<\boldsymbol{{lkkjkbmbbnnb}}}}\right. \\ $$$$\boldsymbol{{jkkhjm}}\sqrt{\boldsymbol{{nlm}}\mathrm{6}\boldsymbol{{jikmbh}}\sqrt{\boldsymbol{{jlbj}}}} \\ $$$$\boldsymbol{{jljbnkbbnmnmmnjknbjnrurubv}}\underset{\boldsymbol{{nkjnbmm}}} {\boldsymbol{{m}}} \\ $$$$\boldsymbol{{jjnbbnjnnj}}^{} \\ $$$$\boldsymbol{{nkn}}…

define-f-x-y-xy-x-2-y-2-x-2-y-2-if-x-y-0-0-0-if-x-y-0-0-show-that-f-f-x-and-f-y-are-continuous-on-R-2-show-that-2-f-x-y-and-

Question Number 132477 by KZ last updated on 14/Feb/21 $${define} \\ $$$${f}\left({x}.{y}\right)= \\ $$$$\left.\left\{\frac{\mathrm{xy}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{if}\:\left({x}.{y}\right)\neq\right)\mathrm{0}.\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\left({x}.{y}\right)=\left(\mathrm{0}.\mathrm{0}\right) \\ $$$$ \\ $$$${show}\:{that}\:{f},\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}\:\:}\:{are}\: \\…

nice-calculus-0-sin-x-2-ln-x-x-3-2-dx-solution-x-2-t-1-2-0-sin-t-ln-t-t-3-4-dt-t-1-2-1-4-0-

Question Number 132459 by mnjuly1970 last updated on 14/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}^{\mathrm{2}} \right){ln}\left({x}\right)}{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx}= \\ $$$$\:\:{solution}: \\ $$$$\boldsymbol{\phi}\overset{{x}^{\mathrm{2}} ={t}} {=}\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}\right){ln}\left(\sqrt{{t}}\:\right)}{{t}^{\frac{\mathrm{3}}{\mathrm{4}}} }\:\frac{{dt}}{{t}^{\frac{\mathrm{1}}{\mathrm{2}}}…