Question Number 61976 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:{A}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{dxdy}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \\…
Question Number 193045 by Trent1111 last updated on 02/Jun/23 $${what}\:{is}\:{the}\:{HCF}\:{of}\: \\ $$$$\mathrm{8}{k}+\mathrm{1}\:{and}\:\mathrm{9}{k}\:?\:{where}\:{k}\:\in\:\mathbb{Z}^{+} \\ $$ Answered by MM42 last updated on 02/Jun/23 $$\left(\mathrm{8}{k}+\mathrm{1},\mathrm{9}{k}\right)={d} \\ $$$${d}\mid\mathrm{8}{k}+\mathrm{1}\:\Rightarrow{d}\mid\mathrm{72}{k}+\mathrm{9}\:\:\: \\…
Question Number 127508 by mohammad17 last updated on 30/Dec/20 Commented by mohammad17 last updated on 30/Dec/20 $${such}\:{that}\:\beta\:{beta}\:{function} \\ $$ Answered by Ar Brandon last updated…
Question Number 127509 by mr W last updated on 30/Dec/20 Commented by mr W last updated on 31/Dec/20 $${if}\:{both}\:{ellipses}\:{have}\:{the}\:{same}\:{shape} \\ $$$${as}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1},\:{determine}\:\frac{{b}}{{a}}=?…
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Question Number 127505 by bramlexs22 last updated on 30/Dec/20 $$\left(\mathrm{y}^{\mathrm{2}} +\mathrm{2x}^{\mathrm{2}} \mathrm{y}\right)\:\mathrm{dx}\:+\:\left(\mathrm{2x}^{\mathrm{3}} −\mathrm{xy}\right)\:\mathrm{dy}\:=\:\mathrm{0} \\ $$ Answered by liberty last updated on 30/Dec/20 $$\:\frac{{dy}}{{dx}}\:=\:\frac{{y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} {y}}{{xy}−\mathrm{2}{x}^{\mathrm{3}}…
Question Number 193037 by DAVONG last updated on 02/Jun/23 Answered by Subhi last updated on 02/Jun/23 $${DC}^{\mathrm{2}} ={DB}.{AD} \\ $$$$\mathrm{20}^{\mathrm{2}} ={DB}.\left(\mathrm{9}+{DB}\right) \\ $$$${DB}^{\mathrm{2}} +\mathrm{9}{DB}−\mathrm{400}=\mathrm{0} \\…
Question Number 193036 by ali009 last updated on 02/Jun/23 $${if}\:{f}\left({x}\right)={x}\sqrt{\left(\mathrm{16}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$${find}\:\int_{\mathrm{0}.\mathrm{5}} ^{\mathrm{3}.\mathrm{5}} {f}\left({x}\right)\:{dx}\:{using}\:{trapezoidal}\:{method} \\ $$$${then}\:{find}\:{the}\:{max}\:{and}\:{min}\:{value}\:{of}\:{the}\:{error} \\ $$$$\:{with}\:{the}\:{given}\:{n}\:{steps} \\ $$$${x}_{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}_{{n}} \right) \\…
Question Number 61966 by aliesam last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −{e}^{−\mathrm{2}{x}} }\:{dx} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} }}{dx}=\int\frac{{e}^{\mathrm{2}{x}} }{{e}^{\mathrm{2}{x}}…
Question Number 127500 by mr W last updated on 30/Dec/20 $${if}\:\mathrm{sin}\:{x}_{\mathrm{1}} +\mathrm{sin}\:{x}_{\mathrm{2}} +…+\mathrm{sin}\:{x}_{\mathrm{100}} =\mathrm{0}, \\ $$$${find}\:{the}\:{maximum}\:{value}\:{of} \\ $$$$\mathrm{sin}^{\mathrm{5}} \:{x}_{\mathrm{1}} +\mathrm{sin}^{\mathrm{5}} \:{x}_{\mathrm{2}} +…+\mathrm{sin}^{\mathrm{5}} \:{x}_{\mathrm{100}} . \\…