Category: Relation and Functions

Question Number 15082 by Tinkutara last updated on 07/Jun/17 $$\mathrm{The}\mathrm{domain}\mathrm{of}f\left(x\right)=\sqrt{x-2\left\{x\right\}}.(\mathrm{where}$$$$\{\cdot \}\mathrm{denotes}\mathrm{fractional}\mathrm{part}\mathrm{of}x)\mathrm{is}?$$ Answered by mrW1 last updated on 07/Jun/17 $$\mathrm{x}=\mathrm{n}+\mathrm{f}$$$$\left\{\mathrm{x}\right\}=\mathrm{f} \…

Question Number 146085 by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{f}(\mathrm{x},\mathrm{y})=\mathrm{x}-\sqrt{\mathrm{x}+2\mathrm{y}}$$$$1)\mathrm{condition}\mathrm{on}\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{to}\mathrm{have}\mathrm{f}\mathrm{symetric}$$$$2)\mathrm{find}\frac{\partial \mathrm{f}}{\partial \mathrm{x}},\frac{\partial \mathrm{f}}{\partial \mathrm{y}},\frac{{\partial }^2\mathrm{f}}{\partial \mathrm{x}\partial \mathrm{y}},\frac{{\partial }^2\mathrm{f}}{\partial \mathrm{y}\partial \mathrm{x}}$$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{x}}\:\mathrm{and}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{y}} \…

Question Number 146087 by mathmax by abdo last updated on 10/Jul/21 $$1)\mathrm{find}{\mathrm{U}}_{\mathrm{n}}={\int }_0^1{\mathrm{x}}^{\mathrm{n}}{\mathrm{e}}^{-2\mathrm{x}}\mathrm{dx}$$$$2)\mathrm{nature}\mathrm{of}\mathrm{\Sigma }{\mathrm{U}}_{\mathrm{n}}?$$ Answered by ArielVyny…

Question Number 146072 by savitar last updated on 10/Jul/21 $$Let{F}_n=2^{2^n}+1thefermatnumber$$$$Provethat$$$$F_{n}isprime\iff 3^{\frac{F_n-1}{2}}\equiv 1\left[F_n\right]$$ Terms of…

Question Number 146041 by alcohol last updated on 10/Jul/21 $$z^{\prime }=2iz+(3-3i)$$$$geometricalrepresentationis?$$ Answered by ajfour last updated on 10/Jul/21 $$\frac{dx}{dt}+i\frac{dy}{dt}=2i(x+iy)+3(1-i)$$$$\Rightarrow\:\frac{{dx}}{{dt}}=\mathrm{3}−\mathrm{2}{y} \…