Question Number 130598 by Lordose last updated on 27/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{x}^{\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{6}} }\mathrm{dx} \\ $$ Answered by mindispower last updated on 27/Jan/21 $$=\frac{\mathrm{1}}{\mathrm{3}}\int_{\mathrm{0}}…
Question Number 130599 by mohammad17 last updated on 27/Jan/21 $${by}\:{using}\:{diffintion}\:{lim}_{{z}\rightarrow\mathrm{1}} \frac{\mathrm{1}}{\mid{z}^{\mathrm{2}} −\mathrm{1}\mid} \\ $$$${help}\:{me}\:{sir} \\ $$ Answered by mathmax by abdo last updated on 27/Jan/21…
Question Number 65062 by ajfour last updated on 24/Jul/19 $${If}\:\:{x}^{\mathrm{4}} +{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\Rightarrow\:{t}^{\mathrm{4}} +{At}^{\mathrm{2}} +{B}=\mathrm{0} \\ $$$${Find}\:{A}\:{and}\:{B}. \\ $$ Commented by MJS last updated…
Question Number 130596 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{equation}\:\mathrm{true}?\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{a}\:+\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{2}} }\:\right)=\:\mathrm{0}. \\ $$ Answered by mr W last updated…
Question Number 65061 by mathmax by abdo last updated on 24/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({x}−{t}\:+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }\:\:{with}\:\:\:{x}>\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{also}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\left({x}−{t}+{t}^{\mathrm{2}} \right)^{\mathrm{4}} } \\…
Question Number 130594 by Lordose last updated on 27/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{1}+\mathrm{x}^{\mathrm{6}} }\mathrm{dx} \\ $$ Answered by mindispower last updated on 27/Jan/21 $$\left.\:\:{existe}\:{if}\:{n}\in\right]−\mathrm{1},\mathrm{5}\left[=\int_{\mathrm{0}} ^{\infty}…
Question Number 65059 by mathmax by abdo last updated on 24/Jul/19 $${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$ Commented by ~ À ® @ 237…
Question Number 130593 by mr W last updated on 27/Jan/21 $${if}\:{a}_{\mathrm{0}} =\mathrm{1},\:{a}_{\mathrm{1}} =\mathrm{2}\:{and}\:{a}_{{n}+\mathrm{1}} =\sqrt{{a}_{{n}} {a}_{{n}−\mathrm{1}} } \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$ Commented by malwan last…
Question Number 65054 by behi83417@gmail.com last updated on 24/Jul/19 $$\begin{cases}{\sqrt{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}+\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}=\boldsymbol{\mathrm{a}}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\boldsymbol{\mathrm{b}}\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right]}\end{cases} \\ $$ Commented by behi83417@gmail.com last updated on 24/Jul/19 $$\mathrm{thanks}\:\mathrm{in}\:\mathrm{advance}\:\mathrm{proph}.\:\mathrm{Abdo}. \\ $$$$\left[\boldsymbol{\mathrm{u}}+\boldsymbol{\mathrm{v}}=\boldsymbol{\mathrm{a}}\Rightarrow\boldsymbol{\mathrm{u}}^{\mathrm{2}} +\boldsymbol{\mathrm{v}}^{\mathrm{2}}…
Question Number 130589 by bramlexs22 last updated on 27/Jan/21 $$\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{identity}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)+\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{x}\right)=\pi/\mathrm{2} \\ $$ Answered by EDWIN88 last updated on 27/Jan/21 $$\:{If}\:{f}\left({x}\right)=\mathrm{tan}^{−\mathrm{1}} \left({x}\right)+\mathrm{cot}^{−\mathrm{1}} \left({x}\right) \\…