Question Number 55268 by maxmathsup by imad last updated on 20/Feb/19 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+\mathrm{3}} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 55269 by maxmathsup by imad last updated on 20/Feb/19 $${let}\:{f}\left({x}\right)\:=\left(\mathrm{2}{x}+\mathrm{1}\right){ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:. \\ $$…
Question Number 186103 by MASANJAJJ last updated on 01/Feb/23 $$\mathrm{Let}\:\mathrm{R}\:\mathrm{denote}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{ordered}\:\mathrm{pairs}\:\left(\mathrm{x},\:\mathrm{y}\right)\: \\ $$$$\mathrm{of}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{x}−\mathrm{y}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integral} \\ $$$$\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{followings}\:\mathrm{ordered}\:\mathrm{pairs} \\ $$$$\mathrm{belong}\:\mathrm{to}\:\mathrm{R}\:\left(\mathrm{9},\mathrm{3}\right)\:\left(\mathrm{3},\:\mathrm{9}\right),\left(\:\mathrm{1}\:,\mathrm{2}\right)\:\left(\mathrm{1},\:\mathrm{5}\right),\left(\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\left(\mathrm{0},\:\mathrm{4}\right),\:\left(\mathrm{4}\:,\mathrm{7}\right). \\ $$$$\left(\mathrm{note}:\:\mathrm{a}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integral}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{b}\:\mathrm{if}\:\mathrm{a}=\mathrm{kb}\right. \\ $$$$\left.\mathrm{whe}{re}\:\mathrm{k}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\right) \\ $$ Terms…
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…