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Category: Algebra

Question-159332

Question Number 159332 by 0731619 last updated on 15/Nov/21 Commented by bobhans last updated on 16/Nov/21 $$\left(\mathrm{1}\right)\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{−} } \:\sqrt{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{undefined}\: \\ $$$$\:\:\:\:\:\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\sqrt{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{−}…

Question-159300

Question Number 159300 by saly last updated on 15/Nov/21 Answered by Derrick last updated on 15/Nov/21 $${preve} \\ $$$$\left.{a}\right){montrons}\:{par}\:{double}\:{inclusion} \\ $$$${soit}\:{x} \\ $$$${x}\in{f}^{−\mathrm{1}} \:\left({A}\cup{B}\right)\Leftrightarrow{f}\left({x}\right)\in\left({A}\cup{B}\right) \\…

Question-28219

Question Number 28219 by math solver last updated on 22/Jan/18 Commented by mrW2 last updated on 22/Jan/18 $${z}={x}+{iy} \\ $$$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{2}{y}\right)^{\mathrm{2}} =\left({x}−\mathrm{1}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}}…

Find-0-x-arctan-x-x-1-x-2-1-dx-

Question Number 159292 by HongKing last updated on 15/Nov/21 $$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{x}\:\mathrm{arctan}\left(\mathrm{x}\right)}{\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}\:\mathrm{dx} \\ $$$$ \\ $$ Answered by mindispower last updated on 15/Nov/21 $$=\int_{\mathrm{0}}…

Question-159281

Question Number 159281 by HongKing last updated on 14/Nov/21 Commented by MJS_new last updated on 14/Nov/21 $${x}=−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{how}? \\ $$$$\mathrm{obviously}\:{x}<\mathrm{0}\:\mathrm{because}\:\mathrm{otherwise}\:\mathrm{lhs}\:>\mathrm{0} \\ $$$$\mathrm{but}\:\mathrm{with}\:{x}=−\mathrm{1}\:\mathrm{lhs}\:<\mathrm{0}\:\Rightarrow\:−\mathrm{1}<{x}<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{I}\:\mathrm{tried}\:{x}=−\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\mathrm{lhs}\:<\mathrm{0}\:\Rightarrow\:−\frac{\mathrm{1}}{\mathrm{2}}<{x}<\mathrm{0}…

Solve-in-R-x-x-2-244x-736-1008-

Question Number 159280 by HongKing last updated on 14/Nov/21 $$\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{in}\:\mathbb{R}\::\:\:\sqrt{\mathrm{x}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{244x}\:+\:\mathrm{736}}{\mathrm{1008}} \\ $$$$ \\ $$ Answered by MJS_new last updated on 14/Nov/21 $$\mathrm{just}\:\mathrm{square}\:\mathrm{and}\:\mathrm{solve}\:\left(\mathrm{and}\:\mathrm{test}\:\mathrm{the}\:\mathrm{solutions}\right) \\ $$$$\Rightarrow…