Category: Relation and Functions

Question Number 55276 by maxmathsup by imad last updated on 20/Feb/19 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{16n^2-1}$$ Commented by maxmathsup by imad last updated…

Question Number 55268 by maxmathsup by imad last updated on 20/Feb/19 $$calculate\sum _{n=0}^{\mathrm{\infty }}\frac{{(-1)}^n}{4n+3}$$ Commented by maxmathsup by imad last updated on…

Question Number 186103 by MASANJAJJ last updated on 01/Feb/23 $$\mathrm{Let}\mathrm{R}\mathrm{denote}\mathrm{a}\mathrm{set}\mathrm{of}\mathrm{all}\mathrm{ordered}\mathrm{pairs}(\mathrm{x},\mathrm{y})$$$$\mathrm{of}\mathrm{integers}\mathrm{such}\mathrm{that}\mathrm{x}-\mathrm{y}\mathrm{is}\mathrm{an}\mathrm{integral}$$$$\mathrm{multiple}\mathrm{of}3.\mathrm{Which}\mathrm{of}\mathrm{the}\mathrm{followings}\mathrm{ordered}\mathrm{pairs}$$$$\mathrm{belong}\mathrm{to}\mathrm{R}(9,3)(3,9),(1,2)(1,5),(7,2)$$$$(0,4),(4,7).$$$$(\mathrm{note}:\mathrm{a}\mathrm{is}\mathrm{an}\mathrm{integral}\mathrm{multiple}\mathrm{of}\mathrm{b}\mathrm{if}\mathrm{a}=\mathrm{kb}$$$$\mathrm{whe}re\mathrm{k}\mathrm{is}\mathrm{an}\mathrm{integer})$$ Terms…

Question Number 54830 by maxmathsup by imad last updated on 12/Feb/19 $$let{V}_n={\int }_0^{\mathrm{\infty }}\frac{cos\left(nx\right)}{n+x^2}dxwithnintegrnsturalnot0.$$$$1)calculate{V}_n$$$$2)calculate{lim}_{n\to +\mathrm{\infty }}{nV}_n$$$$\left.\mathrm{3}\right)\:{calculate}\:{the}\:{sum}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{V}_{{n}}…

Question Number 120300 by bemath last updated on 30/Oct/20 $$Determineallfunctionf:R\to R$$$$whichsatisfyf(a+x)-f(a-x)=4ax$$$$forallrealaandx.$$ Commented by benjo_mathlover last updated on 30/Oct/20 $${let}\:{f}\left({x}\right)={px}^{\mathrm{2}} +{qx}+{r}…