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Question Number 6590 by Temp last updated on 04/Jul/16 $$\mathrm{Solve}\:\mathrm{for}\:{a} \\ $$$$\frac{{a}^{\mathrm{2}} +\mathrm{1}}{{a}}=\frac{{a}}{\mathrm{1}−{a}^{\mathrm{2}} } \\ $$ Commented by nburiburu last updated on 04/Jul/16 $$\mathrm{1}−{a}^{\mathrm{4}} ={a}^{\mathrm{2}}…
Question Number 72118 by psyche last updated on 24/Oct/19 Commented by psyche last updated on 24/Oct/19 $${Question}\:\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 72117 by psyche last updated on 24/Oct/19 $${Please}\:{help}\:{with}\:{the}\:{proof}\:{of}\:{cauchy}\:{inequality}. \\ $$ Commented by Tanmay chaudhury last updated on 24/Oct/19 Terms of Service Privacy Policy…
Question Number 72112 by A8;15: last updated on 24/Oct/19 Answered by mind is power last updated on 24/Oct/19 $$\mathrm{x}=\frac{\mathrm{1}}{\mathrm{t}}\Rightarrow\mathrm{dx}=\frac{−\mathrm{dt}}{\mathrm{t}^{\mathrm{2}} } \\ $$$$\frac{\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{899999999}} }}{\frac{\left(\mathrm{1}+\mathrm{t}^{\mathrm{9}} \right)^{\mathrm{1000000001}} }{\mathrm{t}^{\mathrm{900}\:\mathrm{000009}}…
Question Number 137648 by JulioCesar last updated on 05/Apr/21 Commented by mr W last updated on 05/Apr/21 $$\mathrm{2}+\sqrt{\mathrm{5}} \\ $$ Answered by mr W last…
Question Number 72111 by A8;15: last updated on 24/Oct/19 Commented by mathmax by abdo last updated on 24/Oct/19 $${let}\:{I}=\int_{\mathrm{0}} ^{\frac{{e}}{\pi}} \:\frac{{arctan}\left(\frac{\pi{x}}{{e}}\right)}{\pi{x}\:+{e}}{dx}\:{changement}\:\frac{\pi{x}}{{e}}\:={t}\:{give} \\ $$$${I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctant}}{\pi\left(\frac{{et}}{\pi}\right)+{e}}\frac{{e}}{\pi}{dt}\:=\frac{{e}}{\pi}\int_{\mathrm{0}}…
Question Number 137611 by JulioCesar last updated on 04/Apr/21 Answered by Dwaipayan Shikari last updated on 04/Apr/21 $$\gamma\:\:=\:\mathrm{0}.\mathrm{57721}\:\left({Euler}\:{Mascheroni}\:{constant}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 6535 by Temp last updated on 01/Jul/16 $$\underset{{x}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{x}}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+… \\ $$$$\boldsymbol{\mathrm{Is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{true}}? \\ $$$$\therefore\Sigma\frac{\mathrm{1}}{{x}}=\Sigma\left(\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{\mathrm{2}{x}−\mathrm{1}}\right) \\ $$$$=\Sigma\left(\frac{\mathrm{2}{x}−\mathrm{1}+\mathrm{2}{x}}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right) \\ $$$$=\Sigma\left(\frac{\mathrm{2}{x}−\mathrm{2}+\mathrm{1}+\mathrm{2}{x}}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right) \\ $$$$=\Sigma\left(\frac{\mathrm{4}{x}−\mathrm{2}}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right) \\ $$$$=\Sigma\left(\frac{\mathrm{2}\left(\mathrm{2}{x}−\mathrm{1}\right)}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right) \\…
Question Number 6523 by Tawakalitu. last updated on 30/Jun/16 $$\sqrt{{x}^{{x}^{\mathrm{6}} } }\:\:\:=\:\:\:\mathrm{729} \\ $$$$ \\ $$$${find}\:\:{x} \\ $$ Commented by Rasheed Soomro last updated on…