]> MathML test

# MathML test

My personal MathML test suite. To view the expressions as intended, you need Mozilla and some special fonts.

Pressing and holding the mouse button within, but at the fringes of, the gray, dashed borders should "zoom" the equations.

Here, have a screenshot.

1. $a ⁢ x 2 + b ⁢ x + c = 0$
2. $x 2 + b a ⁢ x + c a = 0$
3. $x 2 + b a ⁢ x = - c a$
4. $x 2 + 2 × x × b 2 ⁢ a = - c a$
5. $x 2 + 2 × x × b 2 ⁢ a + b 2 ⁢ a 2 = - c a + b 2 ⁢ a 2$
6. $x + b 2 ⁢ a 2 = - c × 4 ⁢ a a × 4 ⁢ a + b 2 4 ⁢ a 2$
7. $x + b 2 ⁢ a = b 2 - 4 ⁢ a ⁢ c 4 ⁢ a 2$
8. $x + b 2 ⁢ a = b 2 - 4 ⁢ a ⁢ c 4 ⁢ a 2$

Vs.

$x + b 2 ⁢ a = - b 2 - 4 ⁢ a ⁢ c 4 ⁢ a 2$
9. $x = - b 2 ⁢ a + b 2 - 4 ⁢ a ⁢ c 2 ⁢ a$

Vs.

$x = - b 2 ⁢ a - b 2 - 4 ⁢ a ⁢ c 2 ⁢ a$
10. $x = - b ± b 2 - 4 ⁢ a ⁢ c 2 ⁢ a$

## Definition of the derivative

$f\text{'}\left(x\right)=\underset{\Delta x\to 0}{\text{lim}}\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\Delta x}$

## Choosing without replacement

$\left(\genfrac{}{}{0}{}{n}{r}\right)=\frac{n×\left(n-1\right)×\left(n-2\right)×\text{…}×\left(n-r+1\right)}{1×2×3\text{…}×r}=\frac{n!}{r!\left(n-r\right)!}$

## Hypergeometric probability

$P\left(k\text{elements from}D\right)=\frac{\left(\genfrac{}{}{0}{}{m}{k}\right)\left(\genfrac{}{}{0}{}{n-m}{r-k}\right)}{\left(\genfrac{}{}{0}{}{n}{r}\right)}$

## Distance between two points

$A=\left({x}_{1},{y}_{1}\right)$ $B=\left({x}_{2},{y}_{2}\right)$ $AB=\left|\stackrel{\to }{AB}\right|=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}$

## The power $ax$

The exponent $x$ is Requirements for $a$
a positive integer $a∈R$
zero $a≠0$
a negative integer $a≠0$
a fraction $a>0$
an irrational number $a>0$

$\stackrel{\to }{u}+\stackrel{\to }{v}=\left[{x}_{1},{y}_{1}\right]+\left[{x}_{2},{y}_{2}\right]=\left({x}_{1}×\stackrel{\to }{{e}_{x}}{y}_{1}×\stackrel{\to }{{e}_{y}}\right)+\left({x}_{2}×\stackrel{\to }{{e}_{x}}{y}_{2}×\stackrel{\to }{{e}_{y}}\right)=\left({x}_{1}+{x}_{2}\right)\stackrel{\to }{{e}_{x}}+\left({y}_{1}+{y}_{2}\right)\stackrel{\to }{{e}_{y}}=\left[{x}_{1}+{x}_{2},{y}_{1}+{y}_{2}\right]$
$\underset{a}{\overset{b}{\int }}f\left(x\right)\mathrm{dx}=\underset{n\to \infty }{\text{lim}}\sum _{i=1}^{n}f\left({x}_{i}\right)×\Delta x=\underset{n\to \infty }{\text{lim}}\left(f\left({x}_{1}\right)×\Delta x+f\left({x}_{2}\right)×\Delta x+\text{…}+f\left({x}_{n}\right)×\Delta x\right)$