Question Number 54876 by shaddie last updated on 13/Feb/19 $$\mathrm{find}\:\mathrm{the}\:\mathrm{coefficientof}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{binomial} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{x}}\right)^{\mathrm{4}} \\ $$ Commented by maxmathsup by imad last updated on 13/Feb/19…
Question Number 54830 by maxmathsup by imad last updated on 12/Feb/19 $${let}\:{V}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{{n}\:+{x}^{\mathrm{2}} }{dx}\:\:\:{with}\:{n}\:{integr}\:{nstural}\:{not}\:\mathrm{0}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{V}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} {nV}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{the}\:{sum}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{V}_{{n}}…
Question Number 54821 by Abdo msup. last updated on 12/Feb/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{arctan}\left({nx}\right)}{{n}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 120300 by bemath last updated on 30/Oct/20 $${Determine}\:{all}\:{function}\:{f}:{R}\rightarrow{R} \\ $$$${which}\:{satisfy}\:{f}\left({a}+{x}\right)−{f}\left({a}−{x}\right)=\mathrm{4}{ax} \\ $$$${for}\:{all}\:{real}\:{a}\:{and}\:{x}. \\ $$ Commented by benjo_mathlover last updated on 30/Oct/20 $${let}\:{f}\left({x}\right)={px}^{\mathrm{2}} +{qx}+{r}…
Question Number 120288 by Bird last updated on 30/Oct/20 $${let}\:{f}\left({x}\right)=\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +\mathrm{3}} \\ $$$${determine}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$${and}\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by TITA last updated on…
Question Number 120272 by cantor last updated on 30/Oct/20 $$\varphi\left({x}\right)=\boldsymbol{{x}}^{\boldsymbol{{r}}} \\ $$$$\boldsymbol{{where}}\:\boldsymbol{{x}}\in\left[\mathrm{0},+\infty\left[\:\boldsymbol{{and}}\:\mathrm{0}<\boldsymbol{{r}}\leqslant\mathrm{1}\right.\right. \\ $$$${shown}\:{that}\:{for}\:{any}\:\left(\boldsymbol{{x}},\boldsymbol{{y}}\right)\in\mathbb{R}_{+} ^{\mathrm{2}} \\ $$$$\boldsymbol{\varphi}\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)\leqslant\boldsymbol{\varphi}\left(\boldsymbol{{x}}\right)+\boldsymbol{\varphi}\left(\boldsymbol{{y}}\right) \\ $$$$\:\:\:\:\boldsymbol{{please}} \\ $$ Terms of Service Privacy…
Question Number 185793 by Rupesh123 last updated on 27/Jan/23 Answered by cortano1 last updated on 28/Jan/23 $$\frac{\mathrm{2}}{{x}+\mathrm{1}}\:=\frac{\mathrm{1}}{\mathrm{5}}\Rightarrow{x}=\mathrm{9} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{5}}\right)=\:\mathrm{9}^{\mathrm{2}} −\mathrm{1}=\mathrm{80} \\ $$ Answered by CElcedricjunior…
Question Number 54675 by maxmathsup by imad last updated on 09/Feb/19 $${simplify}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{cos}\left({k}\theta\right)\:{and}\:{B}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{sin}\left({k}\theta\right)\:. \\…
Question Number 185678 by Mingma last updated on 25/Jan/23 Answered by Frix last updated on 25/Jan/23 $${y}^{\mathrm{3}} +\mathrm{2}{y}−{x}=\mathrm{0} \\ $$$$\mathrm{Cardano}'\mathrm{s}\:\mathrm{Formula} \\ $$$${y}=\sqrt[{\mathrm{3}}]{\frac{{x}}{\mathrm{2}}+\sqrt{\frac{{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{\mathrm{8}}{\mathrm{27}}}}−\sqrt[{\mathrm{3}}]{−\frac{{x}}{\mathrm{2}}+\sqrt{\frac{{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{\mathrm{8}}{\mathrm{27}}}} \\…
Question Number 54504 by afachri last updated on 05/Feb/19 $$\boldsymbol{\mathrm{please}},\boldsymbol{\mathrm{Sir}}.\:\:\:\boldsymbol{\mathrm{Would}}\:\boldsymbol{\mathrm{u}}\:\boldsymbol{\mathrm{explain}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{how}}\:? \\ $$$$\boldsymbol{\mathrm{if}}\:\:\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}\:−\:\mathrm{1}}\right)\:\:+\:\:\mathrm{2}\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}\:−\:\mathrm{1}}{\boldsymbol{{x}}}\right)\:\:=\:\:\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}\:−\:\mathrm{1}}\:\:\:, \\ $$$$\boldsymbol{\mathrm{then}}\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:\:\boldsymbol{\mathrm{is}}\:…. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 05/Feb/19 $${f}\left({a}\right)+\mathrm{2}{f}\left(\frac{\mathrm{1}}{{a}}\right)={a}\:×\mathrm{2} \\…