Category: Relation and Functions

Question Number 48065 by maxmathsup by imad last updated on 18/Nov/18 $$letf:]0,1[contnueintegrable{u}_n={(-1)}^n{\int }_0^1{x}^{n}f\left(x\right)dx$$$$provethat\mathrm{\Sigma }{u}_{n}cnvergeandfinditssum$$$$$$ Commented…

Question Number 48009 by maxmathsup by imad last updated on 18/Nov/18 $$let{f}_n\left(t\right)=t^{n-1}sin\left(n\theta \right)withtfrom[0,1[and\theta from[0,\pi [$$$$1)provetheuniformconvergenceof\mathrm{\Sigma }{f}_n\left(t\right)on[0,1[$$$$2)letS\left(t\right)=\mathrm{\Sigma }{f}_n\left(t\right)calculate{\int }_0^{1}S\left(t\right)dt.$$ Terms…

Question Number 178635 by infinityaction last updated on 19/Oct/22 $$\mathrm{solution}\mathrm{set}\mathrm{of}{\log }_{{\mathrm{x}}^2}(\frac{\mathrm{x}}{\mid \mathrm{x}\mid }-\mathrm{x})⩾0$$ Commented by Frix last updated on 19/Oct/22 $$x⩽-2\vee 0<x<1$$ Commented…

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 $$1)calculate{u}_n={\int }_0^{\mathrm{\infty }}{e}^{-nx}ln(1+x)dxwithnintegrnatural$$$$2)calculate{lim}_{n\to +\mathrm{\infty }}{u}_n$$$$3)find\sum _{n=0}^{\mathrm{\infty }}{u}_n$$…