Question Number 219414 by universe last updated on 24/Apr/25 $$\:\:\:\mathrm{given}\:\mathrm{the}\:\mathrm{recursive}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{define}\:\mathrm{by}\:\mathrm{setting} \\ $$$$\:\:\mathrm{a}_{\mathrm{1}\:} \:\in\:\left(\mathrm{0},\mathrm{1}\right)\:\:\:,\:\:\:\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} \left(\mathrm{1}−\mathrm{a}_{\mathrm{n}} \right)\:\:\:,\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\:\:\mathrm{prove}\:\mathrm{that}\:\:\left(\mathrm{1}\right)\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{na}_{\mathrm{n}} =\:\mathrm{1} \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\mathrm{b}_{\mathrm{n}} \:=\:\mathrm{n}\left(\mathrm{1}−\mathrm{na}_{\mathrm{n}} \right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{incresing}\:\mathrm{sequence}…
Question Number 219404 by golsendro last updated on 24/Apr/25 $$\:\:\mathrm{given}\:\mathrm{g}\left(\mathrm{x}\right)=\:\frac{\mathrm{x}−\mathrm{2023}}{\mathrm{x}−\mathrm{1}} \\ $$$$\:\:\mathrm{find}\:\left(\mathrm{gogogogogog}\right)\left(\mathrm{2024}\right) \\ $$ Commented by kapoorshah last updated on 25/Apr/25 $${g}^{−\mathrm{1}} \left({x}\right)=\frac{{x}−\mathrm{2023}}{{x}−\mathrm{1}} \\ $$$$\:\:\:\:\:\left({g}\:{o}\:{g}\:{o}\:{g}\:{o}\:{g}\:{o}\:{g}\:{o}\:{g}\right)\left(\mathrm{2024}\right)…
Question Number 219352 by Spillover last updated on 23/Apr/25 Answered by Spillover last updated on 01/May/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219351 by Spillover last updated on 23/Apr/25 Answered by Spillover last updated on 01/May/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219343 by SdC355 last updated on 23/Apr/25 $$\int\int\int_{\:\mathrm{S}} \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −{z}^{\mathrm{2}} } \:\mathrm{dA}=??? \\ $$ Answered by Nicholas666 last updated on 23/Apr/25 $$\mathrm{4}\pi{R}^{\mathrm{2}}…
Question Number 219281 by Rojarani last updated on 22/Apr/25 Answered by Ghisom last updated on 22/Apr/25 $${P}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{1} \\ $$$${P}\:'\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3} \\ $$$${P}\:''\left({x}\right)=\mathrm{6}{x} \\ $$$$…
Question Number 219315 by mnjuly1970 last updated on 22/Apr/25 $$ \\ $$$$\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{4}} }=? \\ $$ Answered by Nicholas666 last updated on 23/Apr/25…
Question Number 219283 by ea last updated on 22/Apr/25 Answered by Nicholas666 last updated on 22/Apr/25 $$ \\ $$$$\:\:\:\:\frac{\left(−\mathrm{1}\right)^{{m}+\mathrm{1}} {B}_{{m}} }{{e}} \\ $$ Commented by…
Question Number 219304 by ea last updated on 22/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219267 by zetamaths last updated on 21/Apr/25 $${Une}\:{fonction}\:{P}\:{est}\:{dite}\:{quasi}\:{polynomiale}\:{s}'{il}\:{existe}\:\left({pour}\:{k}\in\mathbb{N}\:\right)\:{k}+\mathrm{1}\:{fonction}\:{periodique}\left({c}_{{i}} \right)_{{i}\in\left[\mid\mathrm{0};{k}\mid\right]} {de}\:\mathbb{Z}\:{dans}\:\mathbb{R} \\ $$$$\:{telles}\:{que}\:{P}\left({n}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{c}_{{i}} \left({n}\right){n}^{{i}} \\ $$$$\left(\mathrm{1}\right)\:{Montrez}\:{que}\:{l}'{ensemble}\:{des}\:{fonction}\:{quasi}\:{polynomiale}\:{forme}\:{un}\:\mathbb{R}−{ev}\left({real}\:{space}\:{vector}\right). \\ $$$$\left(\mathrm{2}\right){Montrez}\:{que}\:{si}\:{P},{Q}:\mathbb{Z}\rightarrow\mathbb{R}\:{sont}\:{desfonction}\:{quasi}\:{polynomiale}\:{tel}\:{que}\:{P}\left({n}\right)={Q}\left({n}\right)\:\forall{n}\in\mathbb{N}\:{alors}\:{P}={Q} \\ $$ Answered by…