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Category: Relation and Functions

let-give-s-x-n-1-nx-n-and-w-x-n-1-1-n-x-n-1-for-x-lt-1-find-s-x-w-x-at-form-of-series-2-find-s-x-w-x-at-form-of-function-

Question Number 30407 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:{s}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} {nx}^{{n}} \:\:{and}\:{w}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{n}}{x}^{{n}−\mathrm{1}} \:\:{for}\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{s}\left({x}\right).{w}\left({x}\right)\:{at}\:{form}\:{of}\:{series} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{s}\left({x}\right).{w}\left({x}\right)\:{at}\:{form}\:{of}\:{function}. \\ $$ Terms of…

Use-the-binomial-theorem-to-write-the-first-four-terms-of-the-expansion-of-2-3x-x-2-

Question Number 161442 by nadovic last updated on 18/Dec/21 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{binomial}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{write} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\sqrt{\mathrm{2}+\mathrm{3}{x}−{x}^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on…

let-p-x-1-ix-x-2-n-1-ix-x-2-n-1-determine-roots-of-p-x-2-find-p-x-at-form-a-i-x-i-3-ddtermne-p-x-at-form-arctan-4-factorize-p-x-inside-C-x-5-calculate-0-1-p-x-dxand-1-

Question Number 95837 by mathmax by abdo last updated on 28/May/20 $$\mathrm{let}\:\mathrm{p}\left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} −\left(\mathrm{1}−\mathrm{ix}\:+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{determine}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{at}\:\mathrm{form}\:\Sigma\:\mathrm{a}_{\mathrm{i}} \:\mathrm{x}^{\mathrm{i}} \\ $$$$\left.\mathrm{3}\right)\mathrm{ddtermne}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{at}\:\mathrm{form}\:\mathrm{arctan} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\…

let-f-x-1-x-ln-1-2x-1-calculate-f-n-x-and-f-n-1-2-developp-f-at-integr-serie-at-x-0-1-3-developp-f-at-integr-serie-at-x-0-0-

Question Number 95786 by abdomathmax last updated on 27/May/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{x}}\mathrm{ln}\left(\mathrm{1}+\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie}\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1} \\ $$$$\left.\mathrm{3}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie}\:\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{0} \\ $$ Commented by Rio…