Question Number 125240 by hatakekakashi1729gmailcom last updated on 09/Dec/20 Commented by Dwaipayan Shikari last updated on 09/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {xlog}\left({x}\right)\:{dx}\:\:\:\:\:{logx}={t}\Rightarrow\frac{\mathrm{1}}{{x}}=\frac{{dt}}{{dx}} \\ $$$$=\int_{−\infty} ^{\mathrm{0}} {te}^{\mathrm{2}{t}} \:\:\:{dt}\:\:\:\:\:\mathrm{2}{t}=−{u}…
Question Number 190779 by 07049753053 last updated on 11/Apr/23 $$\boldsymbol{\mathrm{R}{e}}\left(\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{a}}}\right)^{\boldsymbol{{a}}−\mathrm{1}} \\ $$ Answered by Frix last updated on 11/Apr/23 $${f}\left({a}\right)=\left(\frac{\mathrm{1}}{\mathrm{1}−{a}}\right)^{{a}−\mathrm{1}} \in\mathbb{R}\forall{a}<\mathrm{1} \\ $$$$\underset{{a}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{f}\left({a}\right)\:=\mathrm{1} \\…
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Question Number 125230 by mohammad17 last updated on 09/Dec/20 Answered by mathmax by abdo last updated on 09/Dec/20 $$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+..}}}\:\Rightarrow\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{x}+\mathrm{f}\left(\mathrm{x}\right)\:\Rightarrow\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}\right)−\mathrm{x}=\mathrm{0} \\ $$$$\mathrm{withf}\geqslant\mathrm{0}\:\:\:\:\rightarrow\Delta=\mathrm{1}−\mathrm{4}\left(−\mathrm{x}\right)=\mathrm{4x}+\mathrm{1}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}+\sqrt{\mathrm{4x}+\mathrm{1}}}{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}−\sqrt{\mathrm{4x}+\mathrm{1}}}{\mathrm{2}}\:\mathrm{but}\:\mathrm{f}\geqslant\mathrm{0}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}+\sqrt{\mathrm{4x}+\mathrm{1}}}{\mathrm{2}}…
Question Number 190760 by 073 last updated on 10/Apr/23 Answered by mehdee42 last updated on 10/Apr/23 $$\frac{\mathrm{1}}{\mathrm{2}{log}_{{x}} \mathrm{2}}×\frac{\mathrm{1}}{{log}_{{x}} \mathrm{3}}=\frac{\mathrm{1}}{{log}_{{x}} \mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}{log}_{{x}} \mathrm{3}} \\ $$$$\Rightarrow{lg}_{{x}} \mathrm{18}=\mathrm{1}\Rightarrow{x}=\mathrm{18} \\…
Question Number 59682 by aliesam last updated on 13/May/19 $${if} \\ $$$$ \\ $$$${H}={X}^{\mathrm{2}} +{Y}^{\mathrm{2}} +{Z}^{\mathrm{2}} \\ $$$$ \\ $$$${prove} \\ $$$$ \\ $$$$\frac{\partial^{\mathrm{2}} {H}}{\partial{X}^{\mathrm{2}}…
Question Number 125201 by joki last updated on 09/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125199 by joki last updated on 09/Dec/20 Answered by bemath last updated on 09/Dec/20 $${I}=\:\int\:{x}\:\sqrt{\sqrt{\mathrm{4}}\:{x}^{\mathrm{2}} +\pi^{\mathrm{2}} }\:{dx}\:=\: \\ $$$${I}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\int\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\pi^{\mathrm{2}} }\:{d}\left(\mathrm{2}{x}^{\mathrm{2}} +\pi^{\mathrm{2}} \right)…
Question Number 125195 by Eric002 last updated on 09/Dec/20 Answered by mr W last updated on 09/Dec/20 $$\frac{{AD}}{\mathrm{sin}\:\mathrm{58}}=\frac{{DC}}{\mathrm{sin}\:{x}}\:\:\:…\left({i}\right) \\ $$$$\frac{{AD}}{\mathrm{sin}\:\angle{B}}=\frac{{BD}}{\mathrm{sin}\:\mathrm{32}}\: \\ $$$$\angle{B}=\mathrm{180}−\mathrm{58}−{x}+\mathrm{32}=\mathrm{90}−{x} \\ $$$$\frac{{AD}}{\mathrm{cos}\:{x}}=\frac{{DC}}{\mathrm{sin}\:\mathrm{32}}\:\:\:…\left({ii}\right) \\…
Question Number 190730 by 073 last updated on 10/Apr/23 $$\mid\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{18}\mid+\mid\mathrm{y}−\mathrm{3}\mid=\mathrm{5} \\ $$$$\mathrm{all}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}=?? \\ $$$$\mathrm{how}\:\mathrm{money}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{is}\:\mathrm{possible}?? \\ $$ Answered by Frix last updated on 10/Apr/23 $${x}^{\mathrm{2}}…