Question Number 74342 by mathmax by abdo last updated on 22/Nov/19 $$\left.\mathrm{1}\right)\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}} \left[{x}\right]{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{lim}_{{n}\rightarrow+\infty} \:\:{n}\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$ Commented by…
Question Number 74225 by mathmax by abdo last updated on 20/Nov/19 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$ Answered by mind is power…
Question Number 139711 by bramlexs22 last updated on 30/Apr/21 $$\:\left[\mathrm{f}\left(\mathrm{x}\right)\right]^{\mathrm{2}} −\left[\mathrm{f}\left(−\mathrm{x}\right)\right]^{\mathrm{2}} =\mathrm{4x} \\ $$ Commented by mr W last updated on 30/Apr/21 $${f}\left({x}\right)=\frac{{x}}{{a}}+{a} \\ $$…
Question Number 139639 by bemath last updated on 30/Apr/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflection}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{point}\:\left(\mathrm{2},\mathrm{2}\right)\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}+\mathrm{2y}\:=\:\mathrm{4}? \\ $$ Commented by bramlexs22 last updated on 30/Apr/21 $$\mathrm{Let}\:\mathrm{P}\left(\mathrm{2},\mathrm{2}\right)\:\&\:\mathrm{P}'\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflectional} \\ $$$$\mathrm{image}\:\mathrm{of}\:\mathrm{P}\:\mathrm{in}\:\mathrm{L}. \\…
Question Number 139612 by 676597498 last updated on 29/Apr/21 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left(\sqrt{{x}}\right)}{{e}^{\mathrm{2}\pi\sqrt{{x}}} −\mathrm{1}}{dx}\:=\:\mathrm{1}−\frac{{e}}{\left({e}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 139592 by bemath last updated on 29/Apr/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}}\:+\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{If}\:\left(\mathrm{g}\circ\mathrm{f}\right)\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\mathrm{1}\:\mathrm{then}\:\mathrm{g}^{−\mathrm{1}} \left(−\mathrm{1}\right)=? \\ $$ Answered by EDWIN88 last updated on 29/Apr/21 $$\Rightarrow\left(\mathrm{g}\circ\mathrm{f}\right)\left(\mathrm{x}\right)=\:\mathrm{2x}+\mathrm{1}\:;\:\mathrm{g}^{−\mathrm{1}}…
Question Number 74026 by mathmax by abdo last updated on 17/Nov/19 $${U}_{{n}} {is}\:{a}\:{sequence}\:{wich}\:{verfy}\: \\ $$$$\forall{n}\:\in{N}\:\:\:\:\:\:\:\:\mathrm{2}^{{n}} \left(\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} \right)=\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{is}\:\left({U}_{{n}} \right)\:{cojverhent}\:? \\…
Question Number 74019 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{the}\:{matrix}\:\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \:\:{for}\:{n}\:{integr} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:\:{and}\:{e}^{−{A}} . \\ $$ Commented by mathmax by…
Question Number 74016 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{g}\left({x}\right)\:=\frac{\mathrm{1}}{{x}}\int_{{x}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:{arctan}\left({xt}\right){dt} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{g}\left({x}\right)\:\:{and}\:{lim}_{{x}\rightarrow+\infty} {g}\left({x}\right). \\ $$ Commented by mathmax by abdo…
Question Number 74014 by mathmax by abdo last updated on 17/Nov/19 $$\:\: \\ $$$$\:\:{let}\:{W}\left({x}\right)=\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{{x}^{{i}+{j}} }{{ij}} \\ $$$${calculate}\:{W}\:^{'} \left({x}\right). \\ $$ Commented by mathmax by…