Pruebas

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$$\begin{array}{rl}adj(A)adj(adj(A))& =|adj(A)|I_n\\ Aadj(A)adj(adj(A))& =|adj(A)|A{I}_n\\ |A|I_{n}adj(adj(A))& =|adj(A)|A\\ |A|I_{n}adj(adj(A))& =|A{|}^{n-1}A\\ adj(adj(A))& =|A{|}^{n-2}A;|A|\ne 0\end{array}$$

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$$\begin{array}{rl}Aadj(A)& =|A|I_n\\ |Aadj(A)|& =||A|I_n|\\ |A||adj(A)|& =|A{|}^n|I_n|\\ & =|A{|}^n\cdot 1\\ & =|A{|}^n\\ \{\begin{array}{ll}|adj(A)|=|A{|}^{n-1}& ;\text{ Si }A\text{ es no singular }|A|\ne 0\\ |A||adj(A)|=|A{|}^n& ;\text{ Si }A\text{ es singular }\end{array}\end{array}$$

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$$\begin{array}{rl}(adj(A){)}^{-1}& =\frac{adj(adj(A))}{|adj(A)|}\\ & =\frac{|A{|}^{n-1}A}{|A{|}^{n-1}}\\ & =\frac{A}{|A|}\\ & =adj(A{)}^{-1}\end{array}$$

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$$\begin{array}{rl}\underset{x\to 0}{lim}\frac{1-\cos (x))}{x^2}& =\underset{x\to 0}{lim}\frac{1-\cos (x))}{x^2}\cdot \frac{1+\cos (x)}{1+\cos (x)}\\ & =\underset{x\to 0}{lim}\frac{1-{\cos }^2(x)}{x^2}\cdot \frac{1}{1+\cos (x)}\\ & =\underset{x\to 0}{lim}\frac{{\sin }^2(x)}{x^2}\cdot \frac{1}{1+\cos (x)}\\ & =\underset{x\to 0}{lim}\frac{\sin (x)}{x}\cdot \frac{\sin (x)}{x}\cdot \frac{1}{1+\cos (x)}\\ & =1\cdot 1\cdot \frac{1}{2}=\frac{1}{2}\end{array}$$

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When $a\ne 0$, there are two solutions to $a{x}^2+bx+c=0$ and they are $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}.$$

When $a \ne 0$, there are two solutions to $a{x}^2+bx+c=0$ and they are $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}.$$

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$$\begin{array}{rl}\underset{x\to +\mathrm{\infty }}{lim}f(x)& =\underset{x\to +\mathrm{\infty }}{lim}{\displaystyle \frac{(x^2+x+1)}{5x(x-3)}}\\ & =\underset{x\to +\mathrm{\infty }}{lim}{\displaystyle \frac{(x^2+x+1)}{5x^2-15x}}\\ & =\underset{x\to +\mathrm{\infty }}{lim}{\displaystyle \frac{1+\frac{1}{x}+\frac{1}{x^2}}{5-\frac{15}{x}}}=\frac{1}{5}\end{array}$$ $${\int }_0^{\mathrm{\infty }}\frac{x^3}{e^x-1}dx=\frac{{\pi }^4}{15}$$

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https://en.wikibooks.org/wiki/LaTeX/Mathematics https://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm https://tex.stackexchange.com/questions/3/compiling-documents-online/1654#1654 https://latex.codecogs.com/legacy/eqneditor/editor.php?lang=es-es https://www.codecogs.com/latex/eqneditor.php?lang=en-en https://editor.codecogs.com/docs/2-editor_installation.php http://mathurl.com https://jsbin.com https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}\beta\alpha\gamma\ell\Im\Re\Rightarrow\Leftarrow

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• Mendeleiev predijo la existencia de los gases nobles. (135-201)
• Ver solución Ver solución
• Todos los metales alcalinos tiene su único estado de oxidación igual a +1. (172-114)
• Ver solución V
• Todos los halógenos tiene un EOmín = −1 y  un EOmáx = +7. (172-114)
• Ver solución F
• Un elemento de EOmín = −3, típicamente tiene 5 electrones de valencia. (172-114)
• Ver solución (V). 5−8=−3