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Given-an-Elipsis-in-O-i-j-E-x-2-1-4-y-2-1-1-We-admit-that-it-image-by-the-transformation-f-x-2-x-y-y-2-x-y-is-an-elipsis-E-5x-2-5y-2-6xy-8-0-Ca

Question Number 140708 by mathocean1 last updated on 11/May/21 $$\mathrm{Given}\:\mathrm{an}\:\mathrm{Elipsis}\:\mathrm{in}\:\left(\mathrm{O};\overset{\rightarrow} {\mathrm{i}};\overset{\rightarrow} {\mathrm{j}}\right) \\ $$$$\left(\mathrm{E}\right):\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}/\mathrm{4}}+\frac{{y}^{\mathrm{2}} }{\mathrm{1}}=\mathrm{1}.\: \\ $$$${W}\mathrm{e}\:\mathrm{admit}\:\mathrm{that}\:\mathrm{it}\:\mathrm{image}\:\mathrm{by}\:\mathrm{the}\:\mathrm{transformation}\: \\ $$$$\mathrm{f}\::\:\begin{cases}{{x}'=\sqrt{\mathrm{2}}\left({x}+{y}\right)}\\{{y}'=\sqrt{\mathrm{2}}\left(−{x}+{y}\right)\:}\end{cases} \\ $$$${is}\:{an}\:{elipsis}\:\left({E}'\right):\:\mathrm{5}{x}^{\mathrm{2}} +\mathrm{5}{y}^{\mathrm{2}} +\mathrm{6}{xy}−\mathrm{8}=\mathrm{0} \\…

Question-140702

Question Number 140702 by help last updated on 11/May/21 Answered by liberty last updated on 12/May/21 $$\left(\mathrm{3}\right)\:\frac{\mathrm{y}^{\cancel{\mathrm{2}}} }{\mathrm{2}}\:=−\mathrm{x}\cancel{\mathrm{y}}\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\Rightarrow\:−\frac{\mathrm{dx}}{\mathrm{x}}\:=\:\frac{\mathrm{2dy}}{\mathrm{y}} \\ $$$$\Rightarrow−\mathrm{ln}\:\mathrm{x}\:+\:\mathrm{c}\:=\:\mathrm{2ln}\:\mathrm{y}\: \\ $$$$\Rightarrow\:−\mathrm{ln}\:\mathrm{Cx}\:=\:\mathrm{ln}\:\mathrm{y}^{\mathrm{2}} \\…

x-3-1-x-2-dx-

Question Number 140676 by ZiYangLee last updated on 11/May/21 $$\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}=? \\ $$ Answered by Dwaipayan Shikari last updated on 11/May/21 $$\int\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}…

Question-9600

Question Number 9600 by Sopheak last updated on 20/Dec/16 Commented by prakash jain last updated on 20/Dec/16 $${k}^{{th}} \:\mathrm{Term}=\underset{{i}=\mathrm{0}} {\overset{{k}−\mathrm{1}} {\sum}}\mathrm{18}×\left(\mathrm{10}^{\mathrm{2}{i}} \right)=\frac{\mathrm{18}\left(\mathrm{10}^{\mathrm{2}{k}} −\mathrm{1}\right)}{\mathrm{99}} \\ $$$${S}_{{n}}…

dx-x-x-6-x-3-1-

Question Number 140665 by ERA last updated on 11/May/21 $$\int\frac{\mathrm{dx}}{\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{6}} +\mathrm{x}^{\mathrm{3}} +\mathrm{1}}} \\ $$ Answered by MJS_new last updated on 11/May/21 $$\int\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{6}} +{x}^{\mathrm{3}} +\mathrm{1}}}= \\…

Question-140652

Question Number 140652 by mohammad17 last updated on 10/May/21 Answered by TheSupreme last updated on 10/May/21 $${x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}=\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$\int\frac{\mathrm{3}−{x}}{{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}}{dx}=\int\frac{{A}}{{x}−\mathrm{1}}+\frac{{Bx}+{C}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}…