Category: Relation and Functions

Question Number 28169 by abdo imad last updated on 21/Jan/18 $$provethat{\int }_0^1\frac{{\left(lnx\right)}^k}{1-x}dx={(-1)}^k(k!)\xi (k+1).$$ Commented by abdo imad last updated on 23/Jan/18…

Question Number 28138 by abdo imad last updated on 21/Jan/18 $$studieand?givethegraphforthefunction$$$$f\left(x\right)=e^x-x^e.$$ Commented by abdo imad last updated on 26/Jan/18…

Question Number 93418 by abdomathmax last updated on 13/May/20 $$letA=\left(\begin{array}{c}123\\ 321\end{array}\right)\in M_3\left(C\right)$$$$\left(142\right)$$$$1)find{A}^{-1}ifAinversible$$$$2)calculate{A}^n$$$$3)findcosAandsinA$$$$\left.\mathrm{4}\right)\:{is}\:{cos}^{\mathrm{2}} \:{A}\:+{sin}^{\mathrm{2}} \:{A}\:={I}\:? \…

Question Number 93414 by abdomathmax last updated on 13/May/20 $$letp\left(x\right)=\frac{x^n{(4-2x)}^n}{n!}$$$$1)provethat{p}^{\left(k\right)}\left(0\right)=p^{\left(k\right)}\left(2\right)=0forallk\in [1,n-1]$$$$2)provethat\mathrm{\forall }m\in N{p}^{\left(m\right)}\left(0\right)and{p}^{\left(m\right)}\left(2\right)areintegrs$$ Terms of Service…

Question Number 93331 by john santu last updated on 12/May/20 $$\mathrm{If}\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{y}\right)\mathrm{and}$$$$\mathrm{f}\left(1\right)=5\mathrm{then}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}$$$$\mathrm{of}\mathrm{f}\left(2020\right)?$$ Commented by mr W last updated on 12/May/20…