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Category: Relation and Functions

find-f-x-1-f-x-1-x-1-x-3-x-1-2-f-2x-1-x-1-x-2-2x-x-1-3-f-x-1-f-x-y-2f-x-cosy-x-y-f-0-f-pi-2-1-

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…

decompose-inside-C-x-the-fraction-F-x-1-x-2-1-n-with-n-integr-natural-and-n-1-

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…

U-n-is-a-sequence-wich-verify-u-n-u-n-1-1-n-2-1-find-u-n-interms-of-n-2-find-lim-n-u-n-

Question Number 57847 by Abdo msup. last updated on 13/Apr/19 $$\left({U}_{{n}} \right)\:{is}\:{a}\:{sequence}\:{wich}\:{verify}\: \\ $$$${u}_{{n}} +{u}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{u}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} \\ $$…

1-prove-that-arctan-a-arctanb-arctan-a-b-1-ab-with-ab-1-2-find-the-value-of-S-N-n-1-N-1-n-arctan-2n-1-n-2-n-1-

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…

Given-f-x-x-5-ax-4-bx-3-cx-2-dx-c-and-f-1-f-2-f-3-f-4-f-5-Find-a-

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…