HRWiki:Sandbox

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The Sandbox is an HRWiki namespace page designed for testing and experimenting with wiki syntax. Feel free to try your skills at formatting here: click on edit, make your changes, and click 'Save page' when you are finished. Content added here will not stay permanently. If you need help editing, see Help:Editing.

Here are some examples of LaTeX output: 

  • <math>\int\limits_a^x f(\frac{\alpha}{2}\,)\,dx</math>
    produces \int\limits_a^x f(\frac{\alpha}{2}\,)\,dx 
  • <math>\int\limits_1^\infin \frac{1}{k}\,dk</math>
    produces \int\limits_1^\infin \frac{1}{k}\,dk 
  • <math>\sqrt{x^2+2x+1}=|x+1| - \left(\left(\frac{2x^2}{x}\right)^2\right)^2</math>
    produces \sqrt{x^2+2x+1}=|x+1| - \left(\left(\frac{2x^2}{x}\right)^2\right)^2 
  • <math>\sqrt{\sqrt{\sqrt{x}}}</math>
    produces \sqrt{\sqrt{\sqrt{x}}} 
  • <math>\ E = \sum_{i=1}^N e^{- J_{ij} \sigma_i \sigma_j} </math>
    produces \ E = \sum_{i=1}^N e^{- J_{ij} \sigma_i \sigma_j} 
  • <math>\left( \begin{smallmatrix} a&b \\ c&d \end{smallmatrix} \right)</math>
    produces \left( \begin{smallmatrix} a&b \\ c&d \end{smallmatrix} \right) 
  • <math>\therefore</math>
    produces \therefore 
  • <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
    produces x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} 
  • <math>\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a</math>
    produces \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a

\begin{align} \frac{d}{dx}\sin x &= \lim_{dx \to 0} \frac{\sin (x + dx) - \sin x}{dx} \\ &= \lim_{dx \to 0} \frac{\sin x \cos dx + \cos x \sin dx - \sin x}{dx} \\ &= \lim_{dx \to 0} \frac{\cos x \sin dx + \sin x (\cos dx - 1)}{dx} \\ &= \lim_{dx \to 0} \frac{\sin dx}{dx} \cos x + \lim_{dx \to 0} \frac{\cos dx - 1}{dx} \sin x \\ &= \cos x + \lim_{dx \to 0} \frac{\cos dx - 1}{dx} \sin x \\ &= \cos x + \lim_{dx \to 0} \frac {(\cos dx - 1)(\cos dx + 1)}{dx(\cos dx + 1)} \sin x \\ &= \cos x + \lim_{dx \to 0} \frac {(\cos dx)^2 - 1}{dx(\cos dx + 1)} \sin x \\ &= \cos x + \lim_{dx \to 0} \frac {-(\sin dx)^2}{dx(\cos dx + 1)} \sin x \\ &= \cos x + \lim_{dx \to 0} \frac {\sin dx}{dx} \frac{\sin dx}{1} \frac {-1}{(\cos dx + 1)} \sin x \\ &= \cos x + 1 \times 0 \times -\tfrac12 \times \sin x \\ &= \cos x \end{align} 

  • <math>\mbox{if }\overline{AB}\cong\overline{BC}\mbox{ and }\overline{BC}\cong\overline{CD}\mbox{, then }\overline{AB}\cong\overline{CD}</math>
    produces

\mbox{if }\overline{AB}\cong\overline{BC}\mbox{ and }\overline{BC}\cong\overline{CD}\mbox{, then }\overline{AB}\cong\overline{CD}

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