Menu Close

Category: Algebra

Calcular-8-2-8-2-8-

Question Number 150029 by mathdanisur last updated on 08/Aug/21 $$\mathrm{Calcular}: \\ $$$$\sqrt{\mathrm{8}\:+\:\mathrm{2}\sqrt{\mathrm{8}\:+\:\mathrm{2}\sqrt{\mathrm{8}\:+\:…}}}\:=\:? \\ $$ Answered by nimnim last updated on 08/Aug/21 $$\mathrm{Let}\:\sqrt{\mathrm{8}+\mathrm{2}\sqrt{\mathrm{8}+\mathrm{2}\sqrt{\mathrm{8}+……}}}=\mathrm{x} \\ $$$$\Rightarrow\sqrt{\mathrm{8}+\mathrm{2x}}=\mathrm{x} \\…

Find-a-closed-form-a-R-and-a-0-a-0-x-4-1-x-2-1-a-4-x-4-dx-

Question Number 150034 by mathdanisur last updated on 08/Aug/21 $$\mathrm{Find}\:\boldsymbol{\mathrm{a}}\:\mathrm{closed}\:\mathrm{form}:\:\:\boldsymbol{\mathrm{a}}\in\mathbb{R}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{a}}\neq\mathrm{0} \\ $$$$\Omega\left(\mathrm{a}\right)=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{x}^{\mathrm{4}} }{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{a}^{\mathrm{4}} \mathrm{x}^{\mathrm{4}} \right)}\:\mathrm{dx} \\ $$ Answered by mathmax by abdo…

If-x-y-1-2-which-of-the-following-cannot-be-xy-

Question Number 150006 by mathdanisur last updated on 08/Aug/21 $$\mathrm{If}\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{cannot}\:\mathrm{be}\:\:\mathrm{xy}.? \\ $$ Answered by dumitrel last updated on 08/Aug/21 $${xy}={k}\Rightarrow{x}+\frac{{k}}{{x}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\mathrm{2}{x}^{\mathrm{2}} −{x}+\mathrm{2}{k}=\mathrm{0}\Rightarrow\bigtriangleup\geqslant\mathrm{0}\Rightarrow \\ $$$$\mathrm{1}−\mathrm{16}{k}\geqslant\mathrm{0}\Rightarrow{k}\in\left(−\infty;\frac{\mathrm{1}}{\mathrm{16}}\right]\Rightarrow{k}\notin\left(\frac{\mathrm{1}}{\mathrm{16}};\infty\right)…

x-2-x-x-6-1-dx-

Question Number 150007 by mathdanisur last updated on 08/Aug/21 $$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}}{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 08/Aug/21 $${I}=\int\frac{{x}^{\mathrm{2}} +{x}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx}=\int\frac{{x}^{\mathrm{2}}…

lim-x-0-cos-x-1-x-

Question Number 149958 by mathdanisur last updated on 08/Aug/21 $$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt[{\boldsymbol{\mathrm{x}}}]{\mathrm{cos}\sqrt{\mathrm{x}}}\:=\:? \\ $$ Commented by dumitrel last updated on 08/Aug/21 $${e}^{−\frac{\mathrm{1}}{\mathrm{2}}} \\ $$ Commented by…