## Use Equations & Formulas

The Lumen platform currently includes a utility that converts equations and formulas coded in LaTeX both inline (like $x=\frac{1+y}{1+2z^2}$) and separately displayed (like below) as dynamically generated images. The original LaTeX code is included in the image in its “alt” attribute, which you can see by hovering your cursor over the images.

$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$

There are two LaTeX renderers available, one generates cleaner looking images, and the other has the ability to handle more robust mathematical expressions including matrices. Please contact Lumen support for more information on which to use in your course.

The LaTeX code for the equation above is as follows, but note that you must surround the equation or formula with the necessary double dollar sign ($\\\text{equation}\\$) or latex shortcode ($equation$) for it to be dynamically converted:

$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$

Read the official FAQ of the WP LaTeX plugin.

## Common Mathematical Expressions

Here is LaTeX examples for some common expressions you may use.

Adding $\\$ to the beginning and end of this statement:

$\\$ C(g) = \begin{cases} 25 ,\ 0 < g < 2 \\ 25 + 10(g-2) , g \ge 2\\ \end{cases}$\\$

will give: $C(g) = \begin{cases} 25 ,\ 0 < g < 2 \\ 25 + 10(g-2) , g \ge 2\\ \end{cases}$

$\displaystyle{s}=\sqrt{{\frac{{\sum{({x}-\overline{{x}})}^{{2}}}}{{{n}-{1}}}}}{\quad\text{or}\quad}{s}=\sqrt{{\frac{{\sum{f{{({x}-\overline{{x}})}}}^{{2}}}}{{{n}-{1}}}}}$

will give:$\displaystyle{s}=\sqrt{{\frac{{\sum{({x}-\overline{{x}})}^{{2}}}}{{{n}-{1}}}}}{\quad\text{or}\quad}{s}=\sqrt{{\frac{{\sum{f{{({x}-\overline{{x}})}}}^{{2}}}}{{{n}-{1}}}}}$

$\displaystyle{B = \left[\matrix{{1}&{2}&{7}\\{0}&{5}&{6}\\{7}&{8}&{2}}\right]$

will give: $\displaystyle{B = \left[\matrix{{1}&{2}&{7}\\{0}&{5}&{6}\\{7}&{8}&{2}}\right]$

$\text{volume of lead cube}=2.00 cm\times 2.00 cm\times 2.00 cm={\text{8.00 cm}}^{3}$

$\text{volume of lead cube}=2.00 cm\times 2.00 cm\times 2.00 cm={\text{8.00 cm}}^{3}$

$\text{density}=\frac{\text{mass}}{\text{volume}}=\frac{\text{90.7 g}}{{\text{8.00 cm}}^{3}}=\frac{\text{11.3 g}}{{\text{1.00 cm}}^{3}}={\text{11.3 g/cm}}^{3}$

$\text{density}=\frac{\text{mass}}{\text{volume}}=\frac{\text{90.7 g}}{{\text{8.00 cm}}^{3}}=\frac{\text{11.3 g}}{{\text{1.00 cm}}^{3}}={\text{11.3 g/cm}}^{3}$

$4.7\cancel{\text{g}}\text{K}\left(\frac{\text{mol K}}{39.10\cancel{\text{g}}}\right)=0.12\text{mol K}$

$4.7\cancel{\text{g}}\text{K}\left(\frac{\text{mol K}}{39.10\cancel{\text{g}}}\right)=0.12\text{mol K}$