Test the new LaTeX markdown in this Sandbox question!

Question

Purpose of question

We now have \$\LaTeX\$ support through MathJax! Now, instead of writing equations like this:

w0 = 1 / sqrt(L * C)

we can write:

\$\displaystyle \omega_0 = \frac{1}{\sqrt{LC}}\$

Beautiful! However, TeX has a steep learning curve, and it will take some time to figure out how to use this feature. This question is a sandbox in which to practice its use.

Documentation

You'll see in the right sidebar, when writing a question, the line:

MathJaX[sic] equations \$sin^2\theta\$

and a link to generic TeX help. I find that the math mode section is most helpful. The special symbols article is particularly useful:

\$\$ \alpha \beta \mu \Omega \omega \theta \$\$

Note that not all of TeX is included; you'll get this message if you try to include a module that's not in MathJax, such as Tabular:

\$\begin{tabular}1 & 2\\3 & 4\end{tabular}\$

How did they do that?

You can always get at the source by right-clicking an equation. A MathJax context menu will come up, like the following:

and "Show Source" will bring up a window with the source for the equations. Just drop the text contained \$between a pair of escaped dollar signs!\$ Or, you can $$surround it with two dollar signs for centering.$$

This question should be community wiki (No one should get rep from it, and it should be easy to edit), so you can also see the source that way.

Begin \$\LaTeX\$ Sandbox

The markdown for a question should be identical to what you get from an answer, but I'll leave the rest of this question for testing more TeX in case that assumption is mistaken.

Answer 1

Yes, I've been shopping around in various (upvoted) answers, but how about a ...

CHEAT SHEET

To use a formula like \$\frac{Math}{Jax}\$ inline with the text of an answer, surround it with \$, like this:

\$\frac{Math}{Jax}\$

To create a formula centered $$\frac{Math}{Jax}$$ within the article, surround the formula with $$, like this:

$$\frac{Math}{Jax}$$

---

\begin{array}{|c|c|} \text{What you want}&\text{How it is done} \\\hline \\\text{Plain text}&\text{text{Plain text}} \\V_{AC}&\text{V_{AC}} \\Text\ with\ spaces&\text{Text\ with\ spaces} \\\boldsymbol{Bold}&\text{\boldsymbol{Bold}} \\\style{color:green;font-size:300%}A&\text{\style{color:green;font-size:300%}A} \\\alpha&\text{\alpha} \\\beta&\text{\beta} \\\chi&\text{\chi} \\\delta&\text{\delta} \\\Delta&\text{\Delta} \\\epsilon&\text{\epsilon} \\\varepsilon&\text{\varepsilon} \\\eta&\text{\eta} \\\gamma&\text{\gamma} \\\Gamma&\text{\Gamma} \\\digamma&\text{\digamma} \\\varGamma&\text{\varGamma} \\\kappa&\text{\kappa} \\\lambda&\text{\lambda} \\\Lambda&\text{\Lambda} \\\varLambda&\text{\varLambda} \\\mu&\text{\mu} \\\nu&\text{\nu} \\\omega&\text{\omega} \\\Omega&\text{\Omega} \\\varOmega&\text{\varOmega} \\\phi&\text{\phi} \\\Phi&\text{\Phi} \\\varphi&\text{\varphi} \\\varPhi&\text{\varPhi} \\\pi&\text{\pi} \\\Pi&\text{\Pi} \\\varpi&\text{\varpi} \\\varPi&\text{\varPi} \\\psi&\text{\psi} \\\Psi&\text{\Psi} \\\varPsi&\text{\varPsi} \\\rho&\text{\rho} \\\varrho&\text{\varrho} \\\sigma&\text{\sigma} \\\Sigma&\text{\Sigma} \\\varsigma&\text{\varsigma} \\\varSigma&\text{\varSigma} \\\tau&\text{\tau} \\\theta&\text{\theta} \\\Theta&\text{\Theta} \\\varTheta&\text{\varTheta} \\\upsilon&\text{\upsilon} \\\Upsilon&\text{\Upsilon} \\\varUpsilon&\text{\varUpsilon} \\\vartheta&\text{\vartheta} \\\xi&\text{\xi} \\\Xi&\text{\Xi} \\\varXi&\text{\varXi} \\\zeta&\text{\zeta} \\\infty&\text{\infty} \\\approx&\text{\approx} \\\neq&\text{\neq} \\A \oplus B&\text{A \oplus B} \\\%&\text{\%} \\\pm&\text{\pm} \\\triangle&\text{\triangle} \\\Rightarrow&\text{\Rightarrow} \\\Leftarrow&\text{\Leftarrow} \\\rightarrow&\text{\rightarrow} \\\leftarrow&\text{\leftarrow} \\\cos(\varphi)&\text{\cos(\varphi)} \\(j\omega t)^2&\text{(j\omega t)^2} \\R_{max}^2&\text{R_{max}^2} \\R_{max}{}^2&\text{R_{max}{}^2} \\e^{j\omega t+\phi}&\text{e^{j\omega t+\phi}} \\I=\frac{U}{R}&\text{I=\frac{U}{R}} \\P=U\times I&\text{P=U\times I} \\\sqrt{2}&\text{\sqrt{2}} \\I=\sqrt{\frac{P}{R}}&\text{I=\sqrt{\frac{P}{R}}} \\\frac{\partial E}{\partial t}&\text{\frac{\partial E}{\partial t}} \\\sum_{x=1}^{\infty} \frac{1}{x}&\text{\sum_{x=1}^{\infty} \frac{1}{x}} \\1.2\cdot10^{-6}&\text{1.2\cdot10^{-6}} \\\require{cancel} \cancel{2-2}&\text{\require{cancel} \cancel{2-2}} \\\overline{\text{RESET}}&\text{\overline{\text{RESET}}} \\\underline{\text{this}}\text{ is important}&\text{\underline{\text{this}}\text{ is important}} \end{array}

---

The difference between (notice dfrac vs. frac )

\$\dfrac{Math}{Jax}\$ 

and

\$\frac{Math}{Jax}\$ 

gets clear when used in a text paragraph.

The difference between \$\dfrac{Math}{Jax}\$ and \$\frac{Math}{Jax}\$ gets clear when used in a text paragraph.

---

To create a table like the one above:

\begin{array}{|c|c|}
\text{What you want}&\text{How it is done}
\\\hline
\\V_{AC}&\text{V_{AC}}
\end{array}

Answer 2

Entering Units:

\$Because TeX just jams everything together\$,
\$Because TeX just jams everything together\$
...in order to use units well, you need to use the power of the \text{}

e.g.:

ugly:

$$P_{max} = \frac{V_{max}{}^2}{4R_{sink}} = \frac{(150 volts)^2}{4 \times 10 k\Omega} = 9/16 watts$$ $$P_{max} = \frac{V_{max}{}^2}{4R_{sink}} = \frac{(150 volts)^2}{4 \times 10 k\Omega} = 9/16 watts$$

less ugly:

$$P_{max} = \frac{V_{max}{}^2}{4R_{sink}} = \frac{(150 \text{ volts})^2}{4 \times 10\text{ k}\Omega} = 9/16 \text{ watts}$$ $$P_{max} = \frac{V_{max}{}^2}{4R_{sink}} = \frac{(150 \text{ volts})^2}{4 \times 10\text{ k}\Omega} = 9/16 \text{ watts}$$

I don't really like having to put the \Omega outside of the text though, but if it's inside, then it doesn't parse it...

Using \mathrm instead of \text makes commands like \Omega work, but means that spaces must be written as \ :

alternative:

$$P_\mathrm{max} = \frac{V_\mathrm{max}{}^2}{4R_\mathrm{sink}} = \frac{(150\ \mathrm{volts})^2}{4 \times 10\ \mathrm{k\Omega}} = 9/16\ \mathrm{watts}$$ $$P_\mathrm{max} = \frac{V_\mathrm{max}{}^2}{4R_\mathrm{sink}} = \frac{(150\ \mathrm{volts})^2}{4 \times 10\ \mathrm{k\Omega}} = 9/16\ \mathrm{watts}$$

(The technical explanation is that \text switches the TeX parser from "math mode" to "text mode", where the parsing works differently, while \mathrm simply changes the font while staying in math mode.)

Ps. {\rm watts} will also work instead of \mathrm{watts}. Those two commands are basically equivalent, just with different syntax. (\rm is a basic TeX command, while \mathrm is LaTeX. That's pretty much the only difference.)

Answer 3

Subscripts and Superscripts

Easy enough:

• \$R_{max} = 42\$
  • R_{max} = 42
    
    
• \$e^{i\pi} = -1\$
  • e^{i\pi} = -1

What if you want \$R_{max}\$ squared?

• \$R_{max}^2\$
  • R_{max}^2

perhaps not what you wanted, with the subscript and superscript lining up. If you want the superscript to start at the end of the subscript you can jam and empty field(?) to separate them, e.g.:

• \$R_{max}{}^2\$
  • R_{max}{}^2

(from here)

Answer 4

Sets of equations:

\$ \begin{cases} V_6 = \dfrac{R3}{R3+R4} (V_O - V_{IN}) + V_{IN} \\ \\ \\ V_O - V_2 = I_{R2} R2 \\ \\ \\ I_{R2} = j \omega \text{ } C1 (V_2 - V_5) \end{cases}\$

(The extra "\\" are for more vertical spacing)

Over- and underbraces:

\$ z = \overbrace{ \underbrace{x}_\text{real} + \underbrace{iy}_\text{imaginary} }^\text{complex number}\$

Answer 5

Ooh, and if you don't like the serif font, use the sans-serif font (sounds logically, doesn't it?):

\$\mathsf{ C_6H_{12}O_6\ instead\ of\ }C_6H_{12}O_6\$

\$\mathsf{ C_6H_{12}O_6\ instead\ of\ }C_6H_{12}O_6\$

(Also notice the escape \ to create a space in LaTeX's math-mode!)

Answer 6

\$\triangledown \cdot E = \frac{\rho}{\epsilon_0}\$

\$\triangledown \cdot B = 0\$

\$\triangledown \times E = - \frac{\partial B}{\partial t}\$

\$\triangledown \times B = \mu_0 J + \mu_0 \epsilon_0 \frac{\partial E}{\partial t}\$

Pretty sweet...

Answer 7

Tables

Inline math doesn't work for tables: \$begin{array}...\end{array}\$ produces the array on one line:

Apparently, something's changed since this answer was originally written, and tables now work just fine in inline math:

\$ \begin{array}{ccc}x&S(n,x)&x^n \log\left(\frac{x}{x-1}\right)\\-5&-1780484.04&-1780483.95\\-3&-16987.42&-16987.34\\2&709.598&709.783\\ 4&301656.39&301656.52\\6&1.102428722 \times 10^7&1.102428734 \times 10^7\end{array} \$

For arrays, equation arrays, matrices, piecewise equations, aligned equations, and other multi-line constructs, you no longer need to use the displayed math $$..$$ delimiter set, which places the equation on its own line(s):

$$ \begin{eqnarray} f_p(x) & = & \sum_{j=0}^{n} c_j \phi(||x - x_j||) \\ & = & \sum_{j=0}^{n} c_j \phi_j(x) \\ & = & c_0 \phi_0(x) + c_1 \phi_1(x) + \cdots + c_n \phi_n(x) \end{eqnarray} $$

Answer 8

$$ H_{C_1}(s) = \frac {1} {C_1s} $$

$$ H_{R_1}(s) = \frac {T_1s + 1} {C_1s} $$

$$ H_{C_2}(s) = \frac {T_1s + 1} {C_2T_1s^2 + (C_2 + C_1)s} $$

$$ H_{R_2}(s) = \frac {T_1T_2s^2 + (T_1 + T_2 + C_1R_2)s + 1} {T_1C_2s^2 + (C_1 + C_2)s} $$

$$ H_{C_3}(s) = \frac {T_1T_2s^2 + (T_1 + T_2 + C_1R_2)s + 1} {T_1T_2C_3s^3 + ((T_1 + T_2)C_3 + T_1C_2 + C_1R_2C_3)s^2 + (C_1 + C_2 + C_3)s} $$

$$ H_{R_3}(s) = \frac {T_1T_2T_3s^3 + ((T_1 + T_2)T_3 + T_1C_2R_3 + T_3C_1R_2 + T_1T_2)s^2 + (T_1 + T_2 + T_3 + R_3C_2 + R_2C_1 + R_3C_1)s + 1} {T_1T_2C_3s^3 + ((T_1 + T_2)C_3 + T_1C_2 + C_1R_2C_3)s^2 + (C_1 + C_2 + C_3)s} $$

$$ H_{C_4}(s) = \frac {T_1T_2T_3s^3 + ((T_1 + T_2)T_3 + T_1C_2R_3 + T_3C_1R_2 + T_1T_2)s^2 + (T_1 + T_2 + T_3 + R_3C_2 + R_2C_1 + R_3C_1)s + 1} {T_1T_2T_3C_4s^4 + ((T_1 + T_2)T_3C_4 + T_1T_2(C_3 + C_4) + T_1C_2R_3C_4 + T_3C_1R_2C_4)s^3 + ((T_1 + T_2)(C_3 + C4) + T_1C_2 + T_3C_4 + C_1R_2C_3 + R_3C_2C_4 + R_2C_1C_4 + R_3C_1C_4)s^2 + (C_1 + C_2 + C_3 + C_4)s} $$

Wow, this is just great!
First time I was an online page that could print this big (i mean the last one) of a Latex expression. I'm impressed.

But, it is difficult to write. The preview pane flashes between Latex code and Latex images as I type my text. Try editing this message and see for yourself.

---

Matrices and Alignment

Simple Alignment

    \$\begin{matrix}
11 & 12 & 13\\ 
21 & 22 & 23
\end{matrix}\$

\$\begin{matrix} 11 & 12 & 13\\ 21 & 22 & 23 \end{matrix}\$

A Matrix

    \$\begin{bmatrix}
11 & 12 & 13\\ 
21 & 22 & 23
\end{bmatrix}\$

\$\begin{bmatrix} 11 & 12 & 13\\ 21 & 22 & 23 \end{bmatrix}\$

Some Other Matrix Notations

    \$\begin{pmatrix}
11 & 12 & 13\\ 
21 & 22 & 23
\end{pmatrix}\$

\$\begin{pmatrix} 11 & 12 & 13\\ 21 & 22 & 23 \end{pmatrix}\$

    \$\begin{Bmatrix}
11 & 12 & 13\\ 
21 & 22 & 23
\end{Bmatrix}\$

\$\begin{Bmatrix} 11 & 12 & 13\\ 21 & 22 & 23 \end{Bmatrix}\$

Norm

    \$\begin{Vmatrix}
11 & 12 & 13\\ 
21 & 22 & 23
\end{Vmatrix}\$

\$\begin{Vmatrix} 11 & 12 & 13\\ 21 & 22 & 23 \end{Vmatrix}\$

Partial Expressions

    \$f(x) = 
\left\{\begin{matrix}
x; & x \leq 0\\ 
0; & otherwise
\end{matrix}\right.\$

\$f(x) =  \left\{\begin{matrix} x; & x \leq 0\\  0; & otherwise \end{matrix}\right.\$

Multiple Line Alignment

    \$\begin{align}
f(x, y, z) = &   & x^3  & + & 2x^2 & + & x  & + & 3 \\
             & + & 4y^3 &   &      & + & 5x & - & 1 \\
             &   &      & - &  z^2 & - & 2z & + & 2 
\end{align}\$

\$\begin{align} f(x, y, z) = & & x^3 & + & 2x^2 & + & x & + & 3 \\ & + & 4y^3 & & & + & 5x & - & 1 \\ & & & - & z^2 & - & 2z & + & 2 \end{align}\$

---

Usage of Matrices and Alignment in Practice

    $$H(s) = \frac{\sum_{i=0}^{n-1} b_is^i}{s^n + \sum_{i=0}^{n-1} a_is^i} = \frac{b_{n-1}s^{n-1} + b_{n-2}s^{n-2} + b_{n-3}s^{n-3} + \dots + b_0}
{s^n + a_{n-1}s^{n-1} + a_{n-2}s^{n-2} + \dots + a_0}\\
\ \\
\begin{matrix}
\mathbf{\dot{x}} & = & A\mathbf{x} + Bu(t)\\ 
y(t)             & = & C\mathbf{x} + Du(t)
\end{matrix}\\
\ \\
\begin{matrix}
	\begin{bmatrix}
	    \dot{x}_1\\ 
	    \dot{x}_2\\ 
	    \dot{x}_3\\
	    \vdots \\
	    \dot{x}_n
	\end{bmatrix}
	&
	=
	&
	\begin{bmatrix}
	    -b_{n-1} & -b_{n-2} & -b_{n-3} & -b_{n-4} & \cdots & -b_0  \\ 
	    1        & 0        & 0        & 0        & \cdots & 0     \\ 
	    0        & 1        & 0        & \vdots   & \cdots & 0     \\ 
	    0        & 0        & 1        & 0        & \cdots & 0     \\ 
	    \vdots   & \vdots   & 0        & \ddots   & 0      & \vdots\\ 
	    0        & 0        & 0        & 0        & 1      & 0
	\end{bmatrix}
	\begin{bmatrix}
	    x_1\\ 
	    x_2\\ 
	    x_3\\
	    \vdots \\
	    x_n
	\end{bmatrix}
	+
	\begin{bmatrix}
	    1\\ 
	    0\\ 
	    0\\
	    \vdots \\
	    0
	\end{bmatrix}
	u(t)
	\\
	y(t)
	&
	=
	&
	\begin{bmatrix}
	    1 & 0 & 0 & \cdots & 0
	\end{bmatrix}
	\begin{bmatrix}
	    x_1\\ 
	    x_2\\ 
	    x_3\\
	    \vdots \\
	    x_n
	\end{bmatrix}
\end{matrix}$$

Notice that I used nested matrices.

$$H(s) = \frac{\sum_{i=0}^{n-1} b_is^i}{s^n + \sum_{i=0}^{n-1} a_is^i} = \frac{b_{n-1}s^{n-1} + b_{n-2}s^{n-2} + b_{n-3}s^{n-3} + \dots + b_0} {s^n + a_{n-1}s^{n-1} + a_{n-2}s^{n-2} + \dots + a_0}\\ \ \\ \begin{matrix} \mathbf{\dot{x}} & = & A\mathbf{x} + Bu(t)\\ y(t) & = & C\mathbf{x} + Du(t) \end{matrix}\\ \ \\ \begin{matrix} \begin{bmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \vdots \\ \dot{x}_n \end{bmatrix} & = & \begin{bmatrix} -b_{n-1} & -b_{n-2} & -b_{n-3} & -b_{n-4} & \cdots & -b_0 \\ 1 & 0 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \vdots & \cdots & 0 \\ 0 & 0 & 1 & 0 & \cdots & 0 \\ \vdots & \vdots & 0 & \ddots & 0 & \vdots\\ 0 & 0 & 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ x_3\\ \vdots \\ x_n \end{bmatrix} + \begin{bmatrix} 1\\ 0\\ 0\\ \vdots \\ 0 \end{bmatrix} u(t) \\ y(t) & = & \begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ x_3\\ \vdots \\ x_n \end{bmatrix} \end{matrix}$$

---

It crashes if you play with big expressions too much!

It crashed several times until I finish my post.

(My browser: Google Chrome 19.0.1084.56 m)

However, the good thing is, Stack Exchange fully and successfully recovers the lost message after every crash.

Answer 9

Need a new sandbox -- one without cat poop. (Testing comments w/o bugging authors.)

Does this work? Testingtestingtesting

\$\infty\$

\$ \delta_s = \frac{1}{Re\{j\omega \sqrt{\mu \epsilon}\}} \$

Answer 10

How many subscripts can we have? Let's find out.

\$W_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E_{E}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\$

So two things happened: It looks like my answer has left the boundaries of the answer box. It also looks like I make a horizontal scroll bar for this webpage.

Answer 11

\$\LaTeX\$ is superset of \$\TeX\$

Answer 12

This chip costs \$$1.21\$, but an alternative is only \$$0.88\$.

One complaint about using dollar signs is that prices are used too often in electronics questions. Can we at least change it to double-dollar on each end?

Using normal $ signs is no longer a problem. The above sentence looked like this when we used `$ .. $` as the delimiters:

This chip costs \$1.21, but an alternative is only \$0.88.

but this has been fixed. Just use normal dollar signs:

This chip costs $1.21, but an alternative is only $0.88.

If something funny happens to your prose, you've probably got an unmatched delimiter in your equations somewhere. Make sure that \$ only appears around equations.

Answer 13

And if you want to draft/sandbox your MathJax equations on your own PC, Julian Bucknall has a blog post here on how to create an HTML page to do this. It works a treat. Just remember you don't need the \$ delimiters.

Answer 14

\$\style{font-size:700%}\Theta_\style{font-size:700%}\alpha\style{font-size:700%}(\style{font-size:700%}z\style{font-size:700%}) \style{font-size:700%}= \style{font-size:700%}\sum\limits_{n=0,1,2..m}^\infty what\space ? \space \style{color:green;font-size:400%}W? ...\$profit!

Answer 15

Equation numbers (\begin{equation}`, `\end{equation}) not supported

\$\begin{equation}y=x\end{equation}\$

I see no number

Can't make equations in bold by surrounding with asterixes:-

\$Y_{bold}\neq X_{bold}\$

Aha! use \boldsymbol instead

\$\boldsymbol{Y_{bold} = X_{bold}}\$

Answer 16

Wikipedia has a nice summary for displaying a formula

Including a truth table:

\begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}

    \begin{array}{|c|c||c|} a & b & S \\
    \hline
    0&0&1\\
    0&1&1\\
    1&0&1\\
    1&1&0\\
    \end{array}

And I figured out how to align and number formula's:

\$\begin{align} I&=\frac{U}{R}&(1)\\ P & = U×I&(2)\\ & = U × \frac{U}{R}&(3)\\ & = \frac{U^2}{R}&(4) \end{align}\$

    \begin{align}
    I&=\frac{U}{R}&(1)\\
    P & = U×I&(2)\\
      & = U × \frac{U}{R}&(3)\\
      & = \frac{U^2}{R}&(4)
     \end{align}

A simpler way is

$$P=U×I \tag{1}$$

$$P=U×I \tag{1}$$

Answer 17

Here's my try:\$50 \mbox{ }\Omega\$. But that was too short.

Answer 18

$100 <- Testing dollar

Your transformer will convert 120\$V_{ac}\$ to 12\$V_{ac}\$. So you'll need to regulate it to 5\$V_{dc}\$.

• \$I_{ce}\$ = \$I_{be}\$ * HFE

• \$V_{ceo}\$ \$I_{c}MAX\$

• ASCII:
  16 - log((5 - 0)/(5 - 4))/log(2) = 13.68

• TeX:
  \$16 - \frac{log\frac{(5 - 0)}{(5 - 4)}}{log 2} = 13.68\$

• \$I_{F_{max}} = 30mA\$

• \$V_{F_{typ}} = 1.7V\$
• \$V_{F_{max}} = 2.1V\$
• \$V_{R_{max}} = 5V\$

Answer 19

Nested dfracs: \$ \dfrac{ \dfrac{\alpha \beta ^{j2 \pi f t}}{j \omega} }{ \dfrac{\gamma \delta}{\Omega \Phi} } \$ these are meant to create inline equations without resizing them to the size of a single line of text. The line is in effect streched to contain the full equation becoming much higher :)

Answer 20

And you can use Unicode when typing your maths:

$$ A = πr^2 $$

A better way of doing what he did:

$$ P_{max} = \frac{V_{max}{}^2}{4R_{sink}} = \frac{(150 \text{ volts})^2}{4 \times 10\text{ kΩ}} = 9/16 \text{ watts} $$

$$ P_{max} = \frac{V_{max}{}^2}{4R_{sink}} =
   \frac{(150 \text{ volts})^2}{4 \times 10\text{ kΩ}} = 9/16 \text{ watts} $$

Answer 21

This is a test for a bug over on PPCG.

$foo
    $bar
$baz

---

\$foo
    \$bar
\$baz

---

\$foo\$
    \$bar\$
\$baz\$

---

$
foo
bar
baz
$

---

\$
foo
bar
baz
\$

\$ foo bar baz \$

\$ foo bar baz \$

\$ foo bar baz \$

---

Perl, 93 bytes

$_=bpi$=;printf'()'x6x!$`.'
%12s',F.ee x!$\--^substr"\32::\\$&|",-12while/.{$\}/g

Requires the command line option -l71Mbignum=bpi, counted as 14. The \32 should be replaced by a literal character 26.

Sample Usage

$ perl -l71Mbignum=bpi pi-slice.pl
()()()()()()
|\3.1415926|
|:\53589793|
\::\2384626|
 \::\433832|
  \::\79502|
   \::\8841|
    \::\971|
     \::\69|
      \::\3|
       \__\|

---

Perl, 111 bytes

$_=bpi$_*($l=($.=$_)-3);printf'()'x($./2)x!$`."
%$.s",F.ee x!$l--^substr"\32::\\$&|",-$.while/.{$l}/g

Parameterized version. Requires the command line option -nMbignum=bpi, counted as 12.

Sample Usage

$ echo 10 | perl -nMbignum=bpi pi-slice.pl
()()()()()
|\3.14159|
|:\265358|
\::\97932|
 \::\3846|
  \::\264|
   \::\33|
    \::\8|
     \__\|

$ echo 20 | perl -nMbignum=bpi pi-slice.pl
()()()()()()()()()()
|\3.141592653589793|
|:\2384626433832795|
\::\028841971693993|
 \::\75105820974944|
  \::\5923078164062|
   \::\862089986280|
    \::\34825342117|
     \::\0679821480|
      \::\865132823|
       \::\06647093|
        \::\8446095|
         \::\505822|
          \::\31725|
           \::\3594|
            \::\081|
             \::\28|
              \::\4|
               \__\|