Question Number 62812 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left({nt}\right)}{\mathrm{1}+{n}^{\mathrm{2}} {t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:{n}\:{natural}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}}…
Question Number 128346 by Ahmed1hamouda last updated on 06/Jan/21 Answered by MJS_new last updated on 06/Jan/21 $$\int{x}^{\mathrm{2}} \sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\:\rightarrow\:{dx}=\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}}{\mathrm{2}\left(\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\right)}{dt}\right] \\…
Question Number 62811 by mathmax by abdo last updated on 25/Jun/19 $$\left.\mathrm{1}\right)\:{find}\:\:\int\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)}{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)}{dx} \\ $$ Commented by Prithwish…
Question Number 128347 by mathocean1 last updated on 06/Jan/21 $${E}\:{is}\:{a}\:{vectorial}\:{space}\:{wich}\:{has}\:{as}\:{base}\: \\ $$$$\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}},\overset{\rightarrow} {{k}}\right).\: \\ $$$${P}=\left\{\begin{pmatrix}{{x}}\\{{y}}\\{\:{z}}\end{pmatrix}\:{such}\:{that}\:\mathrm{5}{x}+{y}+{z}=\mathrm{0}\right\} \\ $$$$\mathrm{1}.\:{Determinate}\:{one}\:{base}\:{of}\:{P}. \\ $$ Terms of Service Privacy…
Question Number 62809 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{f}\left({x}\right)\:=\:{arctan}\left({nx}\right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by mathmax by abdo…
Question Number 62808 by mathmax by abdo last updated on 25/Jun/19 $${f}\left({t}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{xt}} }{\left({x}+{t}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{set}\:{of}\:{definition}\:{for}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{derivability}\:{of}\:{f} \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\…
Question Number 62806 by mathmax by abdo last updated on 25/Jun/19 $${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 62805 by mathmax by abdo last updated on 25/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} −\mathrm{2}{i}\right)^{\mathrm{2}} }\:{dx} \\ $$ Commented by mathmax by abdo…
Question Number 128341 by liberty last updated on 06/Jan/21 $$\mathrm{Which}\:\mathrm{is}\:\mathrm{larger}\:\mathrm{Z}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{4}}{\mathrm{11}}}}\:\mathrm{or}\:\mathrm{S}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{5}}{\mathrm{11}}}}\:? \\ $$ Commented by mr W last updated on 06/Jan/21 $${without}\:{calculation}: \\ $$$${Z}:\:{larger}\nearrow{smaller}\nearrow{larger} \\ $$$$\Rightarrow{Z}\:{is}\:{larger}\:{than}\:{S}.…
Question Number 128336 by liberty last updated on 06/Jan/21 $$\mathrm{If}\:\:\frac{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}{\mathrm{sec}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}}\:=\:\mathrm{5}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{3cos}\:\mathrm{2x}+\mathrm{1}}{\mathrm{3cos}\:\mathrm{2x}−\mathrm{1}}\:?\: \\ $$ Answered by bramlexs22 last updated on 06/Jan/21 $$\:\Rightarrow\:\frac{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}}{\mathrm{sec}\:{x}−\mathrm{tan}\:{x}}\:=\:\mathrm{5} \\ $$$$\Rightarrow\frac{\mathrm{cos}\:{x}\left(\mathrm{sec}\:{x}+\mathrm{tan}\:{x}\right)}{\mathrm{cos}\:{x}\left(\mathrm{sec}\:{x}−\mathrm{tan}\:{x}\right)}\:=\:\mathrm{5} \\…