Pruebas

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\begin{align*} adj(A) \: adj(adj(A)) &= |adj(A)| \: I_n \\ A\:adj(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 \quad;\quad |A| \neq 0 \\ \end{align*}

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\begin{align*} A\:adj(A) &= |A|\:I_n \\ |A\:adj(A)| &= ||A|\:I_n| \\ |A|\:|adj(A)| &= |A|^n\:|I_n| \\ &= |A|^n \cdot 1\\ &= |A|^n \\ \begin{cases} |adj(A)| = |A|^{n-1} &; \text{ Si } A \text{ es no singular } |A| \neq 0 \\ |A||adj(A)| = |A|^n &; \text{ Si } A \text{ es singular } \end{cases} \end{align*}

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\begin{align*} (adj(A))^{-1} &= \frac{adj(adj(A))}{|adj(A)|} \\ &= \frac{|A|^{n-1}A}{|A|^{n-1}} \\ &= \frac{A}{|A|} \\ &= adj(A)^{-1} \end{align*}

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\begin{align*} \lim\limits_{x \to 0}\frac{1-\cos(x))}{x^2} &= \lim\limits_{x \to 0}\frac{1-\cos(x))}{x^2} \cdot \frac{1+\cos(x)}{1+\cos(x)} \\ &=\lim\limits_{x \to 0}\frac{1-\cos^2(x)}{x^2} \cdot \frac{1}{1+\cos(x)} \\ &=\lim\limits_{x \to 0}\frac{ \sin^2(x)}{x^2} \cdot \frac{1}{1+\cos(x)} \\ &=\lim\limits_{x \to 0}\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{align*}

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When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are \[x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\]

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

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\begin{align*} \lim_{x \rightarrow +\infty} f(x)&=\lim_{x \rightarrow +\infty} \dfrac{(x^2+x+1)}{5x(x-3)} \\ &=\lim_{x \rightarrow +\infty} \dfrac{(x^2+x+1)}{5x^2-15x} \\ &=\lim_{x \rightarrow +\infty} \dfrac{1+\frac{1}{x}+\frac{1}{x^2}}{5-\frac{15}{x}}=\frac{1}{5} \end{align*} \begin{equation} \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15} \label{eq:sample} \end{equation}

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