Question Number 74498 by mathmax by abdo last updated on 25/Nov/19 $$\left.\mathrm{1}\right)\:{calculte}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{nx}} \left[{e}^{{x}} \right]\:{dx}\:\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{{n}} \:{A}_{{n}} \\ $$ Commented by…
Question Number 74499 by mathmax by abdo last updated on 25/Nov/19 $${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 139954 by Ar Brandon last updated on 02/May/21 Answered by mr W last updated on 03/May/21 $${x}_{{n}+\mathrm{1}} =\frac{{x}_{{n}} −\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}}{\mathrm{1}+{x}_{{n}} ×\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}} \\ $$$${let}\:\mathrm{tan}\:{A}_{{n}} ={x}_{{n}}…
Question Number 74353 by mathmax by abdo last updated on 22/Nov/19 $${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}+\sqrt{{k}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{a}\:{equivalent}\:{of}\:{A}_{{n}} \:\:{when}\:{n}\rightarrow+\infty \\ $$$$ \\…
Question Number 74352 by mathmax by abdo last updated on 22/Nov/19 $${let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{k}+\mathrm{1}}\:\:{find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:\:\:\left({n}\rightarrow+\infty\right) \\ $$$$ \\ $$ Answered by mind is…
Question Number 74350 by mathmax by abdo last updated on 22/Nov/19 $${findf}\left({a}\right)=\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({cosx}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{witha}>\mathrm{0} \\ $$ Commented by abdomathmax last updated on 23/Nov/19…
Question Number 74351 by mathmax by abdo last updated on 22/Nov/19 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by ~blr237~ last updated on…
Question Number 74345 by mathmax by abdo last updated on 22/Nov/19 $$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right)=\int_{{x}+\mathrm{1}} ^{{x}^{\mathrm{2}} +\mathrm{1}} \:\:\:{e}^{−{xt}} {arctan}\left({t}\right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:{f}\left({x}\right) \\ $$ Commented by mathmax by…
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…