Category: Relation and Functions

Question Number 112681 by bemath last updated on 09/Sep/20 $$\mathrm{solve}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{function}$$$${\left(\mathrm{f}\left(3\mathrm{x}\right)\right)}^2={\left(\mathrm{f}\left(2\mathrm{x}\right)\right)}^2+{\left(\mathrm{f}\left(\mathrm{x}\right)\right)}^2$$ Answered by bobhans last updated on 09/Sep/20 $$\:\left(\blacklozenge\right)\:\left(\mathrm{f}\left(\mathrm{3x}\right)\right)^{\mathrm{2}} \:=\:\left(\mathrm{f}\left(\mathrm{2x}\right)\right)^{\mathrm{2}}…

Question Number 47063 by maxmathsup by imad last updated on 04/Nov/18 $$1)calculate{u}_n={\int }_0^{\mathrm{\infty }}{e}^{-nx}ln(1+x)dxwithnintegrnatural$$$$2)calculate{lim}_{n\to +\mathrm{\infty }}{u}_n$$$$3)find\sum _{n=0}^{\mathrm{\infty }}{u}_n$$…

Question Number 178032 by TheHoneyCat last updated on 12/Oct/22 $$\bullet D=\{z:\mid z\mid <1\}$$$$\bullet \mathcal{H}(A\to B)\mathrm{denotes}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{holomorfic}$$$$\mathrm{functions}\mathrm{from}A\mathrm{to}B$$$$\bullet \mathrm{We}\mathrm{define}:$$$$W=\{f\in \mathcal{H}(D\to \mathbb{R}):\mid \mid f\mid {\mid }_W<\mathrm{\infty }\}$$$$\mathrm{where}\:\:\mid\mid\:\centerdot\:\mid\mid_{{W}} \::\:\begin{cases}{{W}}&{\rightarrow}&{\mathbb{R}_{+} }\{{f}}&{ }&{\underset{{n}=\mathrm{0}} {\overset{\infty}…

Question Number 46840 by maxmathsup by imad last updated on 01/Nov/18 $$find{lim}_{n\to +\mathrm{\infty }}\sum _{k=1}^n\frac{n^2+k^2}{n^3+k^3}$$ Commented by maxmathsup by…

Question Number 46744 by math khazana by abdo last updated on 31/Oct/18 $$calculate{S}_n=\sum _{0⩽i,j⩽n}\frac{i+j}{2^{i+j}}$$ Commented by MJS last updated on 31/Oct/18…