Category: Relation and Functions

Question Number 111535 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^2-\mathrm{c}\mathrm{satisfy}-4⩽\mathrm{f}\left(1\right)⩽-1$$$$\mathrm{and}-1⩽\mathrm{f}\left(2\right)⩽5,\mathrm{then}$$$$$$$$\mathrm{A}.7⩽\mathrm{f}\left(3\right)⩽26\mathrm{B}.-1⩽\mathrm{f}\left(3\right)⩽20\mathrm{C}.$$$$-4⩽\mathrm{f}\left(3\right)⩽15\mathrm{D}.\frac{-28}{3}⩽\mathrm{f}\left(3\right)⩽\frac{35}{3}\mathrm{E}.$$$$\frac{8}{3}⩽\mathrm{f}\left(3\right)⩽\frac{13}{3}$$…

Question Number 45968 by maxmathsup by imad last updated on 19/Oct/18 $$1)find\sum _{n=1}^{\mathrm{\infty }}\frac{cos\left(nx\right)}{n}and\sum _{n=1}^{\mathrm{\infty }}\frac{sin\left(nx\right)}{n}$$$$2)calculate\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n}cos\left(\frac{2n\pi }{3}\right)and\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n}sin\left(\frac{2n\pi }{3}\right)$$ Commented…

Question Number 45961 by maxmathsup by imad last updated on 19/Oct/18 $$let{f}_n\left(x\right)={(-1)}^{n}ln(1+\frac{x^2}{n(1+x^2)})andf\left(x\right)=\mathrm{\Sigma }{f}_n\left(x\right)$$$$find{lim}_{x\to +\mathrm{\infty }}f\left(x\right).$$ Terms of Service…

Question Number 45960 by maxmathsup by imad last updated on 19/Oct/18 $$findf\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{x^{n}sin\left(nx\right)}{n}$$ Answered by Smail last updated on 22/Oct/18 $${f}\left({x}\right)={Im}\left(\underset{{n}=\mathrm{1}}…

Question Number 45792 by maxmathsup by imad last updated on 16/Oct/18 $$let{u}_n=\sum _{k=1}^n\frac{{(-1)}^{\left[k\right]}}{k}and{H}_n=\sum _{k=1}^n\frac{1}{k}$$$$1)calculate{u}_{n}intermsof{H}_n$$$$\left.\mathrm{2}\right){study}\:{the}\:{convergence}\:{of}\:\left({u}_{{n}} \right)…