Question Number 201653 by mokys last updated on 10/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201654 by mokys last updated on 10/Dec/23 Answered by aleks041103 last updated on 10/Dec/23 $${First}\:{part}: \\ $$$${M}=\begin{pmatrix}{\mathrm{4}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{2}}\end{pmatrix}\: \\ $$$${eigenvals}: \\ $$$${det}\left({M}−{xI}\right)=\begin{vmatrix}{\mathrm{4}−{x}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{2}−{x}}\end{vmatrix}=\mathrm{0} \\ $$$$\Rightarrow\left({x}−\mathrm{4}\right)\left({x}+\mathrm{2}\right)−\mathrm{3}=\mathrm{0}…
Question Number 201712 by esmaeil last updated on 10/Dec/23 Commented by mr W last updated on 11/Dec/23 Commented by mr W last updated on 11/Dec/23…
Question Number 201708 by Calculusboy last updated on 10/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201646 by Calculusboy last updated on 10/Dec/23 Answered by aleks041103 last updated on 10/Dec/23 $$\sqrt[{{ln}\left({x}\right)}]{{x}}={x}^{\frac{\mathrm{1}}{{ln}\left({x}\right)}} =\left({e}^{{ln}\left({x}\right)} \right)^{\frac{\mathrm{1}}{{ln}\left({x}\right)}} ={e}={const} \\ $$$$\Rightarrow\int\sqrt[{{ln}\left({x}\right)}]{{x}}\:{dx}\:=\:{ex}\:+\:{C} \\ $$ Terms…
Question Number 201707 by ajfour last updated on 10/Dec/23 Answered by mr W last updated on 11/Dec/23 Commented by mr W last updated on 11/Dec/23…
Question Number 201702 by hardmath last updated on 10/Dec/23 $$\mathrm{Find}: \\ $$$$\int_{\mathrm{1}} ^{\:\mathrm{3}} \:\mathrm{dx}\:\int_{\boldsymbol{\mathrm{x}}} ^{\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} } \:\left(\mathrm{x}\:−\:\mathrm{y}\right)\:\mathrm{dy} \\ $$ Commented by mr W last updated…
Question Number 201693 by naka3546 last updated on 10/Dec/23 Answered by mr W last updated on 10/Dec/23 Commented by mr W last updated on 10/Dec/23…
Question Number 201689 by cherokeesay last updated on 10/Dec/23 Answered by witcher3 last updated on 10/Dec/23 $$\mathrm{x}^{\mathrm{3}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{12x}−\mathrm{32}=\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{3}} −\mathrm{24} \\ $$$$\mathrm{x}−\mathrm{2}=\mathrm{y} \\ $$$$\Leftrightarrow\sqrt[{\mathrm{3}}]{\mathrm{y}+\mathrm{24}}=\mathrm{y}^{\mathrm{3}} −\mathrm{24}…
Question Number 201680 by cortano12 last updated on 10/Dec/23 $$\:\:\:\Subset \\ $$ Answered by Calculusboy last updated on 11/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{substitute}}\:\boldsymbol{{ditectly}},\:\boldsymbol{{we}}\:\boldsymbol{{get}}\:\frac{\mathrm{0}}{\mathrm{0}}\left(\boldsymbol{{indeterminant}}\right) \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{p}}=\mathrm{2}\boldsymbol{{sinx}}−\boldsymbol{{sim}}\mathrm{2}\boldsymbol{{x}}\:\:\:\:\:\frac{\boldsymbol{{dp}}}{\boldsymbol{{dx}}}=\mathrm{2}\boldsymbol{{cosx}}−\mathrm{2}\boldsymbol{{cos}}\mathrm{2}\boldsymbol{{x}} \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{q}}=\boldsymbol{{sinx}}−\boldsymbol{{xcosx}}\:\:\:\frac{\boldsymbol{{dq}}}{\boldsymbol{{dx}}}=\boldsymbol{{cosx}}−\left(\boldsymbol{{cosx}}−\boldsymbol{{xsinx}}\right) \\…