Question Number 15086 by Tinkutara last updated on 07/Jun/17 $$\mathrm{The}\:\mathrm{range}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\sqrt{\frac{\mathrm{10}^{{x}} \:−\:\mathrm{10}^{\mathrm{4}} }{\mathrm{10}^{{x}} \:+\:\mathrm{10}^{\mathrm{2}} }}\:\mathrm{is}? \\ $$ Answered by ajfour last updated on 07/Jun/17 $$\:{f}\left({x}\right)=\sqrt{\mathrm{1}−\left(\frac{\mathrm{10}^{\mathrm{4}} +\mathrm{10}^{\mathrm{2}}…
Question Number 15082 by Tinkutara last updated on 07/Jun/17 $$\mathrm{The}\:\mathrm{domain}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\sqrt{{x}\:−\:\mathrm{2}\left\{{x}\right\}}.\:\left(\mathrm{where}\right. \\ $$$$\left.\left\{\centerdot\right\}\:\mathrm{denotes}\:\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:{x}\right)\:\mathrm{is}? \\ $$ Answered by mrW1 last updated on 07/Jun/17 $$\mathrm{x}=\mathrm{n}+\mathrm{f} \\ $$$$\left\{\mathrm{x}\right\}=\mathrm{f} \\…
Question Number 15084 by Tinkutara last updated on 07/Jun/17 $$\mathrm{The}\:\mathrm{domain}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{−{x}^{\mathrm{2}} \:+\:\left\{{x}\right\}}}; \\ $$$$\left(\mathrm{where}\:\left\{\centerdot\right\}\:\mathrm{denotes}\:\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:{x}\right) \\ $$$$\mathrm{is}? \\ $$ Answered by mrW1 last updated on 07/Jun/17 $$\mathrm{x}=\mathrm{n}+\mathrm{f}…
Question Number 146085 by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}−\sqrt{\mathrm{x}+\mathrm{2y}} \\ $$$$\left.\mathrm{1}\right)\mathrm{condition}\:\mathrm{on}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{to}\:\mathrm{have}\:\mathrm{f}\:\mathrm{symetric} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\frac{\partial\mathrm{f}}{\partial\mathrm{x}}\:,\frac{\partial\mathrm{f}}{\partial\mathrm{y}}\:,\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{x}\partial\mathrm{y}}\:,\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{y}\partial\mathrm{x}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{x}}\:\mathrm{and}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{y}} \\…
Question Number 146083 by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{F}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{n}} \:−\mathrm{e}^{\mathrm{in}\alpha} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{roots}\:\mathrm{of}\:\mathrm{F}\left(\mathrm{x}\right)? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{F}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 146087 by mathmax by abdo last updated on 10/Jul/21 $$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{n}} \:\mathrm{e}^{−\mathrm{2x}} \:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\mathrm{nature}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} ? \\ $$ Answered by ArielVyny…
Question Number 146082 by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{p}\left(\mathrm{x}\right)=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} −\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{roots}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right)? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$ Terms of Service Privacy…
Question Number 146072 by savitar last updated on 10/Jul/21 $${Let}\:{F}_{{n}} =\mathrm{2}^{\mathrm{2}^{{n}} } +\mathrm{1}\:{the}\:{fermat}\:{number} \\ $$$${Prove}\:{that} \\ $$$$\:{F}_{{n}} \:{is}\:{prime}\:\Leftrightarrow\:\mathrm{3}^{\frac{{F}_{{n}} −\mathrm{1}}{\mathrm{2}}} \equiv\mathrm{1}\left[{F}_{{n}} \right] \\ $$ Terms of…
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Question Number 146041 by alcohol last updated on 10/Jul/21 $${z}'\:=\:\mathrm{2}{iz}\:+\:\left(\mathrm{3}−\mathrm{3}{i}\right) \\ $$$${geometrical}\:{representation}\:{is}? \\ $$ Answered by ajfour last updated on 10/Jul/21 $$\frac{{dx}}{{dt}}+{i}\frac{{dy}}{{dt}}=\mathrm{2}{i}\left({x}+{iy}\right)+\mathrm{3}\left(\mathrm{1}−{i}\right) \\ $$$$\Rightarrow\:\frac{{dx}}{{dt}}=\mathrm{3}−\mathrm{2}{y} \\…