Question Number 189053 by mathlove last updated on 11/Mar/23 $${find}\:{f}\left({x}\right) \\ $$$$\mathrm{1}:{f}\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}+\mathrm{3};\:{x}\neq\mathrm{1} \\ $$$$\mathrm{2}:{f}\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}\:;{x}\neq\mathrm{1} \\ $$$$\mathrm{3}:{f}\left({x}+\mathrm{1}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){cosy}\:\forall{x},{y} \\ $$$${f}\left(\mathrm{0}\right)={f}\left(\frac{\pi}{\mathrm{2}}\right)=\mathrm{1} \\ $$ Answered by cortano12 last…
Question Number 57925 by maxmathsup by imad last updated on 14/Apr/19 $${solve}\:{y}^{''} \:−{xy}\:=\mathrm{0}\:\:{by}\:{using}\:{integr}\:{series}. \\ $$ Commented by maxmathsup by imad last updated on 18/Apr/19 $${let}\:{search}\:{develloppable}\:{at}\:{integr}\:{serie}\:\:{let}\:{y}\:=\sum_{{n}=\mathrm{0}}…
Question Number 57923 by maxmathsup by imad last updated on 14/Apr/19 $${decompose}\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{{x}^{{n}} }{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:{inside}\:{C}\left({x}\right)\:{and}\:{R}\left({x}\right) \\ $$ Commented by maxmathsup by imad last updated on 28/Apr/19…
Question Number 57922 by maxmathsup by imad last updated on 14/Apr/19 $${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$${and}\:{n}\geqslant\mathrm{1} \\ $$ Commented by maxmathsup by imad last updated…
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Question Number 57847 by Abdo msup. last updated on 13/Apr/19 $$\left({U}_{{n}} \right)\:{is}\:{a}\:{sequence}\:{wich}\:{verify}\: \\ $$$${u}_{{n}} +{u}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{u}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} \\ $$…
Question Number 57848 by Abdo msup. last updated on 13/Apr/19 $$\left.\mathrm{1}\right){prove}\:{that}\:{arctan}\left({a}\right)\:+{arctanb}\:={arctan}\left(\frac{{a}+{b}}{\mathrm{1}−{ab}}\right)\: \\ $$$${with}\:{ab}\neq\mathrm{1} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:{S}_{{N}} =\:\sum_{{n}=\mathrm{1}} ^{{N}} \left(−\mathrm{1}\right)^{{n}} \:{arctan}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}−\mathrm{1}}\right) \\ $$ Commented by maxmathsup…
Question Number 57647 by maxmathsup by imad last updated on 09/Apr/19 $${find}\:\:{approximate}\:{value}\:{of}\:\xi\left(\mathrm{3}\right)\:{by}\:{using}\:\:\:{n}−\mathrm{1}\:\leqslant{n}\leqslant{n}+\mathrm{1}\:\:\:{for}\:{n}\:{integr} \\ $$$${natural}\:. \\ $$ Commented by maxmathsup by imad last updated on 18/Apr/19…
Question Number 188651 by cortano12 last updated on 04/Mar/23 $$\:\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{5}} +\mathrm{ax}^{\mathrm{4}} +\mathrm{bx}^{\mathrm{3}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{c} \\ $$$$\:\mathrm{and}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{f}\left(\mathrm{2}\right)=\mathrm{f}\left(\mathrm{3}\right)=\mathrm{f}\left(\mathrm{4}\right)=\mathrm{f}\left(\mathrm{5}\right). \\ $$$$\:\mathrm{Find}\:\mathrm{a}. \\ $$ Answered by horsebrand11 last updated…
Question Number 57529 by maxmathsup by imad last updated on 06/Apr/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{3}} \left({n}+\mathrm{1}\right)} \\ $$ Commented by maxmathsup by imad last updated…