Question Number 135536 by islamo last updated on 13/Mar/21 $$\left(\boldsymbol{{u}}^{\boldsymbol{{v}}} \right)'=? \\ $$$${u}\:,{v}\:\:\:{tow}\:{fonctions} \\ $$ Answered by Olaf last updated on 13/Mar/21 $${u}^{{v}} \:=\:{e}^{\mathrm{ln}\left({u}^{{v}} \right)}…
Question Number 69995 by behi83417@gmail.com last updated on 29/Sep/19 $$\:\:\mathrm{1}.\begin{cases}{\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} }+\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} }=\boldsymbol{\mathrm{a}}}\\{\sqrt{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}+\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}=\boldsymbol{\mathrm{b}}}\end{cases}\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}^{+} \right] \\ $$$$ \\ $$$$\:\:\:\mathrm{2}.\begin{cases}{\sqrt{\sqrt{\mathrm{x}}+\mathrm{y}}+\sqrt{\mathrm{x}+\sqrt{\mathrm{y}}}=\boldsymbol{\mathrm{a}}}\\{\sqrt{\sqrt{\mathrm{x}}−\mathrm{y}}+\sqrt{\mathrm{x}−\sqrt{\mathrm{y}}}=\boldsymbol{\mathrm{b}}}\end{cases} \\ $$$$\: \\ $$$$\:\:\:\mathrm{3}.\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\left(\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{b}}\right)\boldsymbol{\mathrm{xy}}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{3}}…
Question Number 135532 by mr W last updated on 13/Mar/21 Commented by mr W last updated on 13/Mar/21 $${an}\:{old}\:{question} \\ $$ Answered by Dwaipayan Shikari…
Question Number 4446 by Rasheed Soomro last updated on 28/Jan/16 $$\mathrm{Define}\:\mathrm{2}^{\sqrt{\mathrm{3}}} \:\mathrm{and}\:\mathrm{3}^{\sqrt{\mathrm{2}}} \:. \\ $$ Commented by Yozzii last updated on 29/Jan/16 $${Dedekind}\:{cuts}\:{of}\:{the}\:{real}\:{line}\:{might} \\ $$$${define}\:{each}\:{of}\:{those}\:{numbers}.\:…
Question Number 4445 by Rasheed Soomro last updated on 28/Jan/16 $$\mathrm{A}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:\:\:\:\frac{\mathrm{3}}{\mathrm{2}},\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{5}}{\mathrm{4}},\frac{\mathrm{4}}{\mathrm{5}},…. \\ $$$$\mathrm{Write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{general}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{sequence}\:\mathrm{and}\:\mathrm{find}\:\mathrm{its}\:\mathrm{limit}. \\ $$ Commented by 123456 last updated on…
Question Number 4441 by Rasheed Soomro last updated on 27/Jan/16 $$\mathrm{Determine}\: \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{1}/\mathrm{x}} \:. \\ $$ Commented by Yozzii last updated on 29/Jan/16 $${The}\:{limit}\:{does}\:{not}\:{exist}.…
Question Number 4430 by alib last updated on 24/Jan/16 $$\left\{\left({x}−{y}\right)\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)=\mathrm{3}{a}^{\mathrm{2}} \right. \\ $$$$\left({x}+{y}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{15}{a}^{\mathrm{2}} \\ $$$$ \\ $$$${Solve}\:{the}\:{system}\:{of}\:{equation} \\ $$$$ \\ $$…
Question Number 4423 by Rasheed Soomro last updated on 24/Jan/16 $$\mathrm{Determine}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{such}\:\mathrm{that}\:\forall\:\mathrm{t}\in\mathbb{Z} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{8x}+\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{has}\:\mathrm{integer}-\mathrm{solution}. \\ $$ Commented by Yozzii last updated on 24/Jan/16 $${Try}\:{f}\left({t}\right)={c};\:{c}\:{is}\:{a}\:{real}\:{constant}. \\…
Question Number 135493 by EDWIN88 last updated on 13/Mar/21 $$\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{2}}\:=\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\left(\mathrm{1}\right)\begin{cases}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}\geqslant\mathrm{0}}\\{{x}^{\mathrm{2}} −{x}−\mathrm{2}\geqslant\mathrm{0}}\\{{x}^{\mathrm{2}}…
Question Number 135486 by EDWIN88 last updated on 13/Mar/21 $$\frac{\sqrt{\mathrm{2x}+\mathrm{1}}+\sqrt{\mathrm{x}−\mathrm{1}}}{\:\sqrt{\mathrm{2x}+\mathrm{1}}−\sqrt{\mathrm{x}−\mathrm{1}}}\:=\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{x}+\mathrm{2}}}\: \\ $$ Commented by benjo_mathlover last updated on 13/Mar/21 $${wrong} \\ $$$$ \\ $$ Commented…