Just an informative message. We have enabled \LaTeX formatting for mathematical notation on discourse. Encase valid latex math inside dollar symbols and you can create fractions, super- and subscripts, roots, and a lot more:
For example, this notation:
$\frac{(12+144+20)+(3 \cdot \sqrt{4})}{7} + (5 \cdot 11)=9^2+0$
Yields:
\frac{(12+144+20)+(3 \cdot \sqrt{4})}{7} + (5 \cdot 11)=9^2+0
Latex \ is^{sexy}
Yep.
\lim_{x\to 0}{\frac{e^x-1}{2x}} \overset{\left[\frac{1+\sqrt{5}}{2}\right]}{\underset{\mathrm{H}}{=}} \lim_{x\to 0}{\frac{e^x}2}=\underbrace{ \{\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + ... \}}_\text{an infinite sum}
i am not sure what limits you are posting here can you describe that?
copying the latex expression from here is a bit fiddly, it seems to work when i activate plain source as the math renderer, but i have to switch back… not very comfortable.
\left[ \begin{array}{c} r_{0} \\ \theta \\ z \end{array} \right]\; =\; \left[ \begin{array}{c} 3+\sin t+\cos u \\ 2t \\ \sin u+2\cos t \end{array} \right],\; t=0…2\pi ,\; u=0…2\pi
toroid
I was just posting nonsense that looked interesting*, because my original example was so simplistic. It was also a limerick, but nobody noticed that:
A dozen, a gross and a score,
plus three times the square root of four,
divided by seven,
plus five times eleven,
equals nine squared and not a bit more.
* I mean if you forget about the gunk around the equals symbol it’s all true, but not very interesting or succinct. The limit of x going to zero of those two function is \frac{1}{2}.
cool
\begin{align}
\oint_{|z|=2}f(z)\,dz&=\oint_{|z|=R}f(z)\,dz\\\\
&=\oint_{|z|=R} z^2\sqrt{1-\frac{1}{z^3}}\,dz\\\\
&=\oint_{|z|=R} z^2\left(1-\frac{1}{2z^3}+O\left(\frac{1}{z^6}\right)\right)\,dz\\\\
&=\int_0^{2\pi}R^2e^{i2\phi}\left(1-\frac{1}{2R^3e^{i3\phi}}+O\left(\frac{1}{R^6}\right)\right)\,iRe^{i\phi}\,d\phi\\\\
&=-i\pi+O\left(\frac1{R^3}\right)\\\\
&\to -i\pi \,\,\text{as}\,\,R\to \infty \;\;\;\;\;\; _\text{I really like this David}
\end{align}
