Question Number 78286 by msup trace by abdo last updated on 15/Jan/20 $${find}\:{A}_{{n}} =\int\int_{\left[\mathrm{0},{n}\left[\right.\right.} \:\:{e}^{−\left({x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} \right)} {sin}\left({x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} \right){dxdy} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{n}\:{A}_{{n}}…
Question Number 78280 by msup trace by abdo last updated on 15/Jan/20 $${find}\:{by}\:{recurrence} \\ $$$${J}_{{n},{p}} \:=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \left({arctanx}\right)^{{p}} {dx} \\ $$$${stydy}\:{the}\:{serie}\:\sum_{{n}\geqslant\mathrm{0}\:{and}\:{p}\geqslant\mathrm{0}} \:\:{J}_{{n},{p}} \\ $$…
Question Number 78261 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx}\:\:{calculate} \\ $$$${U}_{{n}} \:+{U}_{{n}+\mathrm{1}} \\ $$ Commented by jagoll…
Question Number 78263 by msup trace by abdo last updated on 15/Jan/20 $${find}\:{lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} {sin}\left(\frac{\mathrm{1}}{{k}+{n}}\right) \\ $$ Commented by jagoll last updated on 15/Jan/20…
Question Number 143730 by mathmax by abdo last updated on 17/Jun/21 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{sin}\left(\mathrm{sin}\left(\mathrm{1}−\mathrm{cosx}\right)\right)−\mathrm{1}+\mathrm{cos}\left(\mathrm{x}−\mathrm{sinx}\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$ Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{sin}{x}={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+{o}\left({x}^{\mathrm{4}}…
Question Number 143702 by henderson last updated on 17/Jun/21 $${n}\:\in\:\mathrm{IN}. \\ $$$${I}_{{n}} \:=\:\int_{\mathrm{1}} ^{\:\mathrm{e}} {x}^{{n}+\mathrm{1}} {lnx}\:{dx}. \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\left(\boldsymbol{{I}}_{\boldsymbol{{n}}} \right)\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{increasing}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{part}}−\boldsymbol{\mathrm{by}}−\boldsymbol{\mathrm{part}}\:\boldsymbol{\mathrm{integration}},\:\boldsymbol{\mathrm{calculate}}\:\boldsymbol{{I}}_{\boldsymbol{{n}}} . \\ $$ Answered…
Question Number 78136 by msup trace by abdo last updated on 14/Jan/20 $${give}\:{the}\:{equation}\:{of}\:{tangente} \\ $$$${at}\:\:{p}\left({x}_{\mathrm{0}} ,{f}\left({x}_{\mathrm{0}} \right)\right) \\ $$$$\left.\mathrm{1}\right){f}\left({x}\right)={e}^{−{x}^{\mathrm{2}} } {ln}\left(\mathrm{1}−\mathrm{2}{x}\right)\:\:\:{x}_{\mathrm{0}} =−\mathrm{1} \\ $$$$\left.\mathrm{2}\right){f}\left({x}\right)=\left({x}^{\mathrm{2}} −\mathrm{3}\right){arctan}\left({x}^{\mathrm{2}}…
Question Number 143606 by bobhans last updated on 16/Jun/21 Answered by TheHoneyCat last updated on 16/Jun/21 $${f}\:\mathrm{surjective}\:\Leftrightarrow\:\:\left[\mathrm{1},\:+\infty\left[\subset{f}\left(\mathbb{R}\right)\right.\right. \\ $$$$ \\ $$$$\mathrm{knowing}\:\mathrm{that}\:{f}\in\mathscr{C}^{\mathrm{0}} \left(\mathbb{R},\left[\mathrm{1},+\infty\left[\right)\right.\right. \\ $$$$\mathrm{and}\:\mathrm{that}\:\:{f}\left({x}\right)\underset{{x}\rightarrow\mp\infty} {\rightarrow}+\infty…
Question Number 143576 by Mathspace last updated on 15/Jun/21 $${find}\:{L}\left(\frac{{arctanx}}{{x}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143575 by Mathspace last updated on 15/Jun/21 $${find}\:{L}\left({e}^{−\sqrt{{x}}} \right) \\ $$ Answered by Dwaipayan Shikari last updated on 15/Jun/21 $$\mathscr{L}\left({e}^{−\sqrt{{x}}} \right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}}…