Question Number 199666 by sonukgindia last updated on 07/Nov/23 Answered by witcher3 last updated on 07/Nov/23 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{a}} }{\mathrm{1}+\mathrm{x}^{\mathrm{b}} }\mathrm{dx}\:\mathrm{x}\rightarrow\mathrm{0}\:\frac{\mathrm{x}^{\mathrm{a}} }{\mathrm{1}+\mathrm{x}^{\mathrm{b}} }\sim\mathrm{x}^{\mathrm{a}} \:\mathrm{cv}\:\mathrm{if}\:\mathrm{only}\:\mathrm{if}?\mathrm{a}>−\mathrm{1}..\mathrm{true} \\…
Question Number 199694 by Mingma last updated on 07/Nov/23 Answered by witcher3 last updated on 07/Nov/23 $$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{f}\left(\frac{\mathrm{x}+\mathrm{b}}{\mathrm{2}}\right)−\frac{\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{b}\right)}{\mathrm{2}} \\ $$$$\mathrm{g}\left(\mathrm{a}\right)=\mathrm{0},\mathrm{g}\left(\mathrm{b}\right)=\mathrm{0},\mathrm{rohll}\:\mathrm{theorem} \\ $$$$\left.\Rightarrow\exists\mathrm{c}\in\right]\mathrm{a},\mathrm{b}\left[\mid\mathrm{g}'\left(\mathrm{c}\right)=\mathrm{0};\right. \\ $$$$\mathrm{g}'\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{f}'\left(\frac{\mathrm{x}+\mathrm{b}}{\mathrm{2}}\right)−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{f}'\left(\mathrm{x}\right) \\ $$$$\mathrm{g}'\left(\mathrm{c}\right)=\mathrm{0}\Leftrightarrow\mathrm{f}'\left(\frac{\mathrm{c}+\mathrm{b}}{\mathrm{2}}\right)=\mathrm{f}'\left(\mathrm{c}\right)\:\mathrm{applie}\:\mathrm{Rohll}\:\mathrm{to}…
Question Number 199662 by cortano12 last updated on 07/Nov/23 $$ \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{moves}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{5}}\:\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{it}'\mathrm{s}\:\mathrm{x}−\mathrm{coordinate}\:\mathrm{increases}\: \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{3}\sqrt{\mathrm{10}}\:\:\mathrm{cm}/\mathrm{s}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{it}'\mathrm{s} \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{0}\right) \\ $$$$\mathrm{when}\:\mathrm{x}\:=\:\mathrm{2}…
Question Number 199688 by cortano12 last updated on 07/Nov/23 Commented by cortano12 last updated on 07/Nov/23 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{formula} \\ $$ Answered by AST last updated on…
Question Number 199686 by MathedUp last updated on 07/Nov/23 $${Can}\:{you}\:{help}\:{me}..???\:{pls}…. \\ $$$$\: \\ $$$$\: \\ $$$$\mathrm{Evaluate}\:\int\int_{\:\boldsymbol{\mathcal{S}}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\hat {\boldsymbol{\mathrm{S}}} \\ $$$$\mathrm{Parametric}\:\mathrm{Surface} \\ $$$$\hat {\boldsymbol{\mathrm{S}}}\left({u},{v}\right)=\left(\mathrm{2}+\mathrm{sin}\left({u}\right)\right)\mathrm{cos}\left({v}\right)\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}}…
Question Number 199608 by mathlove last updated on 06/Nov/23 $$\left.\mathrm{1}\right)\:\:\:\mathrm{3}<\mid\mathrm{2}{x}−\mathrm{1}\mid<\mathrm{7}\:\:{find}\:\Sigma{x}\:\:\:\:;{x}\in{Z} \\ $$$$\left.\mathrm{2}\right)\:\:\:\mathrm{4}\leqslant\mid{x}−\mathrm{2}\mid<\mathrm{5}\:\:{find}\:\Sigma{x}\:\:\:\:;{x}\in{Z} \\ $$$$ \\ $$ Answered by mr W last updated on 06/Nov/23 $$\left.\mathrm{1}\right)…
Question Number 199642 by mokys last updated on 06/Nov/23 Commented by mokys last updated on 07/Nov/23 $${whers}\:{steps} \\ $$ Commented by Frix last updated on…
Question Number 199638 by witcher3 last updated on 06/Nov/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{cos}\left(\mathrm{max}\left(\mathrm{x}^{\mathrm{3}} ,\mathrm{y}^{\frac{\mathrm{3}}{\mathrm{2}}} \right)\right)\mathrm{dxdy}=\mathrm{A} \\ $$$$\mathrm{old}\:\mathrm{Quation}\:\mathrm{By}\:\mathrm{mr},\mathrm{univers} \\ $$$$\mathrm{x}^{\mathrm{3}} =\mathrm{t},\mathrm{y}^{\frac{\mathrm{3}}{\mathrm{2}}} =\mathrm{s} \\ $$$$\mathrm{A}=\frac{\mathrm{2}}{\mathrm{9}}\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 199632 by hardmath last updated on 06/Nov/23 In a swimming pool there are four pipes that fill it with water. When pipes 1,…
Question Number 199624 by pascal889 last updated on 06/Nov/23 Commented by mr W last updated on 06/Nov/23 $${you}\:{have}\:{posted}\:{the}\:{same}\:{question} \\ $$$${one}\:{time}\:{and}\:{a}\:{comment}\:{was}\:{given}. \\ $$$${why}\:{don}'{t}\:{you}\:{check}\:{if}\:{your}\:{question} \\ $$$${is}\:{wrong}?\:{maybe}\:{the}\:{question}\:{is} \\…