Question Number 108000 by ZiYangLee last updated on 13/Aug/20 $$\mathrm{If}\:\mathrm{x},\mathrm{y}>\mathrm{0}\: \\ $$$$\mathrm{log}\:\mathrm{x}+\mathrm{log}\:\mathrm{y}=\mathrm{2}, \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}} \\ $$ Answered by mr W last updated on 13/Aug/20 $$\mathrm{ln}\:{xy}=\mathrm{2}…
Question Number 173532 by 0731619 last updated on 13/Jul/22 Answered by solvasky last updated on 14/Jul/22 $${posons}\:{I}=\underset{\pi} {\overset{\pi^{\mathrm{2}} } {\int}}\:\underset{{x}} {\overset{\:{x}^{\mathrm{3}} } {\int}}\underset{−{y}^{\mathrm{2}} } {\overset{\:\:\:\:\:\:\:{y}^{\mathrm{2}}…
Question Number 107993 by mohammad17 last updated on 13/Aug/20 Answered by hgrocks last updated on 13/Aug/20 $$\infty \\ $$ Commented by mohammad17 last updated on…
Question Number 173522 by Gbenga last updated on 12/Jul/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$$$\boldsymbol{\mathrm{evaluate}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173516 by SANOGO last updated on 12/Jul/22 $${calcul} \\ $$$$\int_{{o}} ^{+{oo}} \frac{{tlnt}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$ Answered by aleks041103 last updated on 12/Jul/22…
Question Number 173515 by Muktarr last updated on 12/Jul/22 Answered by aleks041103 last updated on 12/Jul/22 $${U}_{{rms}} =\sqrt{\frac{\mathrm{1}}{{T}}\int_{\mathrm{0}} ^{\:{T}} {U}^{\mathrm{2}} \left({t}\right){dt}} \\ $$$${U}\left({t}\right)=\begin{cases}{+\mathrm{10},\:\mathrm{0}<{t}<{T}/\mathrm{2}}\\{−\mathrm{10},\:{T}/\mathrm{2}<{t}<{T}}\end{cases} \\ $$$$\Rightarrow{U}^{\mathrm{2}}…
Question Number 173507 by JordanRoddy last updated on 12/Jul/22 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$${solve}\:\:\:{y}−\left({x}+\mathrm{1}\right)\:{y}'\:+\:\frac{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:=\:\mathrm{0} \\ $$$$\mathrm{and}\:\:\:\:\:\:{x}\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\:{y}'\:+\left(\frac{{x}}{\mathrm{2}}\:+\mathrm{1}\right)\:{y}\:=\:\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$$$…
Question Number 173493 by mokys last updated on 12/Jul/22 $$\boldsymbol{{find}}\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{0}} \:\boldsymbol{{tan}}\left(\boldsymbol{{tanhx}}\right)−\boldsymbol{{tanh}}\left(\boldsymbol{{tanx}}\right) \\ $$ Answered by aleks041103 last updated on 12/Jul/22 $${just}\:{substitute} \\ $$$${tan}\left({tanh}\left(\mathrm{0}\right)\right)={tan}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${tanh}\left({tan}\left(\mathrm{0}\right)\right)={tanh}\left(\mathrm{0}\right)=\mathrm{0}…
Question Number 173484 by mokys last updated on 12/Jul/22 $$\left.\mathrm{1}\right)\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{0}} \:\frac{\boldsymbol{{x}}^{\boldsymbol{{sinx}}} −\left(\boldsymbol{{sinx}}\right)^{\boldsymbol{{x}}} }{\boldsymbol{{x}}^{\boldsymbol{{cosx}}} +\mathrm{1}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\infty} \:\left[\boldsymbol{{x}}\:\boldsymbol{{lnx}}\:−\:\mathrm{2}\boldsymbol{{x}}\:\boldsymbol{{ln}}\left(\boldsymbol{{sin}}\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}\right)\:\right] \\ $$$$ \\ $$$$\boldsymbol{{how}}\:\boldsymbol{{can}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{proplem}}\:? \\ $$…
Question Number 107946 by ZiYangLee last updated on 13/Aug/20 $$\mathrm{Let}\:\mathrm{a}\:\mathrm{sequence}\:\left\{{a}_{\mathrm{n}} \right\}\:\mathrm{satisfies} \\ $$$${a}_{\mathrm{n}} =\begin{cases}{\mathrm{2},\:\mathrm{n}=\mathrm{1}}\\{\mathrm{2ln}\left({a}_{\mathrm{n}−\mathrm{1}} \right)+\frac{\mathrm{1}}{{a}_{\mathrm{n}−\mathrm{1}} }\:,\:\mathrm{n}\geqslant\mathrm{2}}\end{cases} \\ $$$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$${a}_{\mathrm{n}} \geqslant\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\in\mathbb{N}. \\ $$ Terms of…