Question Number 135377 by Bird last updated on 12/Mar/21 $${solve}\:{x}^{\mathrm{2}} {y}^{''} +\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+\mathrm{3}{y}\:={e}^{−{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135373 by Bird last updated on 12/Mar/21 $${determine}\:{the}\:{sequence}\:{u}_{{n}} \\ $$$${wich}\:{verify}\:{u}_{{n}} \:+{u}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135378 by Bird last updated on 12/Mar/21 $${compare}\:{without}\:{calculator} \\ $$$$\mathrm{5}\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{7}}}−\mathrm{1}\right)\:{and}\:\mathrm{7}\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{5}}}−\mathrm{1}\right) \\ $$ Answered by mr W last updated on 12/Mar/21 $$\mathrm{5}\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{7}}}−\mathrm{1}\right)<\mathrm{5}\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{9}}}−\mathrm{1}\right)=\mathrm{5} \\ $$$$…
Question Number 135375 by Bird last updated on 12/Mar/21 $${let}\:\varphi\left({x}\right)=\frac{{arctan}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{3}} \\ $$$${developp}\:\varphi\:{at}\:{integr}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135369 by Bird last updated on 12/Mar/21 $${let}\:{f}\left({x}\right)={e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{3}+{x}\right) \\ $$$$\left.\mathrm{1}\left.\right)\:{calculate}\:{f}^{\left({n}\right.} \right)\left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 135371 by Bird last updated on 12/Mar/21 $${let}\:{f}\left({x}\right)={tan}\left(\mathrm{2}{x}\right) \\ $$$${ddvelopp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135370 by Bird last updated on 12/Mar/21 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{cosx}\:+\mathrm{2}{sinx}} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69803 by Abdo msup. last updated on 28/Sep/19 $$\left.\mathrm{1}\right){find}\:\:\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\alpha{x}\right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{f}\left({n}\right) \\ $$…
Question Number 69795 by mathmax by abdo last updated on 27/Sep/19 $${let}\:{p}\left({x}\right)=\left({x}+{in}\right)^{{n}} −{n}^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$ Commented by mathmax…
Question Number 69794 by mathmax by abdo last updated on 27/Sep/19 $${let}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{\mathrm{6}} \:−{e}^{{i}\alpha} \:\:\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right){inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorize}\:{p}\left({x}\right){inside}\:{R}\left[{x}\right] \\ $$ Commented by mathmax…