Category: Relation and Functions

Question Number 51996 by maxmathsup by imad last updated on 01/Jan/19 $$calculate{S}_n=\sum _{k=0}^{n-1}sin(\frac{\pi }{4n}+\frac{k\pi }{2n})$$$$$$ Commented by Abdo msup. last updated…

Question Number 51985 by maxmathsup by imad last updated on 01/Jan/19 $$1)letpintegrnaturalnot0calculatearctan\left(\frac{p}{p+1}\right)-arctan\left(\frac{p-1}{p}\right)$$$$2)let{S}_n=\sum _{p=1}^{n}arctan\left(\frac{1}{2p^2}\right)find{lim}_{n\to +\mathrm{\infty }}{S}_n$$ Commented by Abdo msup.…

Question Number 117518 by bobhans last updated on 12/Oct/20 $$\mathrm{f}(\mathrm{x}+1)+\mathrm{xf}(1-\mathrm{x})={\mathrm{x}}^2$$$${\mathrm{f}}^{-1}\left(\mathrm{x}\right)=?$$ Answered by bemath last updated on 12/Oct/20 $$\mathrm{replace}\mathrm{x}+1\mathrm{by}\mathrm{x}$$$$\left(\mathrm{ii}\right)\:\mathrm{f}\left(\mathrm{x}\right)+\left(\mathrm{x}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{1}−\left(\mathrm{x}−\mathrm{1}\right)\right)=\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}}…

Question Number 51983 by maxmathsup by imad last updated on 01/Jan/19 $$fisarealfunctionderivableat0andf\left(0\right)=0find$$$${lim}_{n\to +\mathrm{\infty }}\sum _{k=1}^{n}f\left(\frac{k}{n^2}\right).$$ Terms of Service Privacy Policy…

Question Number 117508 by bemath last updated on 12/Oct/20 $$\mathrm{f}(\mathrm{x}+1)+\mathrm{f}(\mathrm{x}-1)={\mathrm{x}}^2$$$$\mathrm{find}{\mathrm{f}}^{-1}\left(\mathrm{x}\right)=?$$ Answered by bobhans last updated on 12/Oct/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}…