Category: Relation and Functions

Question Number 99580 by mathmax by abdo last updated on 21/Jun/20 $$\mathrm{let}\mathrm{A}=\left(\begin{array}{c}2-1\\ 31\end{array}\right)$$$$1)\mathrm{prove}\mathrm{that}\mathrm{A}\mathrm{is}\mathrm{inversible}\mathrm{and}\mathrm{calculste}{\mathrm{A}}^{-1}$$$$2)\mathrm{calculate}{\mathrm{A}}^{\mathrm{n}}$$$$3)\mathrm{find}{\mathrm{e}}^{\mathrm{A}}\mathrm{and}{\mathrm{e}}^{-\mathrm{A}}$$$$4)\mathrm{calculate}\cos \mathrm{A}\mathrm{and}\mathrm{sinA}\mathrm{is}{\cos }^2\mathrm{A}+{\sin }^2\mathrm{A}=\mathrm{I}?$$$$…

Question Number 34013 by math khazana by abdo last updated on 29/Apr/18 $$find\sum _{n=0}^{\mathrm{\infty }}\frac{cos\left((2n+1)\frac{\pi }{4}\right)}{{(2n+1)}^2}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 33997 by rahul 19 last updated on 29/Apr/18 $$\mathit{I}\mathrm{f}\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{the}\mathrm{function}$$$$\mathrm{f}\left(x\right)=\frac{x-1}{\mathrm{p}-x^2+1}\mathrm{does}\mathrm{not}\mathrm{contain}\mathrm{any}$$$$\mathrm{values}\mathrm{belonging}\mathrm{to}\mathrm{the}\mathrm{interval}$$$$[-1,\frac{-1}{3}]thentrueset\mathrm{of}\mathrm{values}\mathrm{of}\mathrm{p}\mathrm{is}?$$ Answered by ajfour last updated…

Question Number 33985 by abdo imad last updated on 28/Apr/18 $$provethat\frac{1}{1+cosx}=2\sum _{n=1}^{\mathrm{\infty }}n{(-1)}^{n-1}cos\left(nx\right)for$$$$x\ne k\pi ,k\in Z.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 33944 by rahul 19 last updated on 28/Apr/18 $$\mathbf{I}\mathrm{f}\mathrm{the}\mathrm{equation}$$$$({\mathrm{p}}^2-4)({\mathrm{p}}^2-9)x^3+\left[\frac{\mathrm{p}-2}{2}\right]x^2+(\mathrm{p}-4)(\mathrm{p}-3)(\mathrm{p}-2)x+\{2\mathrm{p}-1\}=0.$$$$\mathrm{is}\mathrm{satisfied}\mathrm{by}\mathrm{all}\mathrm{values}\mathrm{of}x\mathrm{in}(0,3]then$$$$sumofallpossibleintegralvaluesof$$$${}^{\prime }{p}^{\prime }is?$$$$\left\{.\right\}\:=\:{fractional}\:{part}\:{function}.…