Question Number 62225 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{j}\:={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{and}\:{P}\left({x}\right)\:=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{P}\left({x}\right)\:{at}\:{form}\:{of}\:{arctan} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){factorize}\:{inside}\:{C}\left[{x}\right]\:\:{the}\:{polynome}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{P}\left({x}\right){dx} \\…
Question Number 62210 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{f}\left({x}\right)\:=\left({x}+\mathrm{1}\right)^{{n}} \:{arctan}\left({nx}\right) \\ $$$${calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$ Commented by mathmax by abdo last updated…
Question Number 62206 by maxmathsup by imad last updated on 17/Jun/19 $${study}\:{the}\:{convergence}\:{of}\:\sum_{{n}\geqslant\mathrm{0}} \:\left(−\mathrm{1}\right)^{{n}} \left\{\left[\sqrt{{n}^{\mathrm{2}} +\mathrm{2}}\right]−\left[\sqrt{{n}^{\mathrm{2}} \:+\mathrm{1}}\right]\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62204 by maxmathsup by imad last updated on 17/Jun/19 $${study}\:{the}\:{convergence}\:{of}\:\:\:\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{e}^{−{n}^{\mathrm{2}} } \right)}{{n}^{{n}} } \\ $$ Commented by maxmathsup by imad last updated…
Question Number 62205 by maxmathsup by imad last updated on 17/Jun/19 $${study}\:{the}\:{convergence}\:{of}\:\:\sum_{{n}\geqslant\mathrm{1}} \:\:\:{n}^{\mathrm{2}} \:{arctan}\left(\mathrm{1}+{e}^{−{n}} \right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62202 by maxmathsup by imad last updated on 17/Jun/19 $${study}\:{the}\:{convergence}\:{of}\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{\sqrt{{n}+\mathrm{1}}−\sqrt{{n}}}{{nln}\left({n}+\mathrm{1}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62199 by maxmathsup by imad last updated on 17/Jun/19 $${let}\:{f}\left({x}\right)\:={e}^{−\frac{\mathrm{1}}{{x}}} \:\:\:\:\:{determine}\:{f}^{\left({n}\right)} \:{by}\:{relation}\:{of}\:{recurrence}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62129 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\mathrm{2}\sqrt{{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int{f}\:\left({x}\right){dx}\:{and}\:\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$ Commented by arcana last…
Question Number 62035 by maxmathsup by imad last updated on 14/Jun/19 $${study}\:{the}\:{sequence}\:\:{U}_{{n}+\mathrm{1}} =\sqrt{{U}_{{n}} \:+\frac{\mathrm{1}}{{n}+\mathrm{1}}}\:\:{with}\:\:{U}_{\mathrm{0}} =\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62003 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{with}\:{x}>\mathrm{1}\:\:{prove}\:{that}\:\:\xi\left({x}\right)\:=\prod_{{p}\:{prime}} \:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−{x}} } \\ $$ Terms of Service Privacy Policy Contact:…