*Due Monday, September 11, 11:59pm*

#### What is $\LaTeX$?

Throughout the semester, youâ€™ll be asked to submit complete written solutions in your own posts on the OpenLab. One way to do this is to upload a photo of work you wrote on paper and upload it as a picture to include in your post. You could also just type the work directly into your post. The regular keyboard can do a lot, but it wonâ€™t look that great and youâ€™ll be missing useful math characters like $\int$ and $\frac{d}{dx}$.

Instead, you can use the most commonly used math typesetting language, called $\LaTeX$ (pronounced LAY-teck) right in your OpenLab posts. $\LaTeX$ is a software system/markup language for typesetting math. It’s used widely to prepare research papers, technical reports, and other documents requiring mathematical symbols. A lot of you are planning on going into technical fields, and might find getting to know how to typeset math in $\LaTeX$ to be useful. It takes a while to learn, but it’s waaaaaay better than Microsoft Word’s equation editor!

Our OpenLab page has a $\LaTeX$ plugin installed, so that’s why I can type beautiful things that look like this:

$u= \int \frac{3-6t}{e^{-t}}dt$

$\quad=\int \left(3e^t – 6te^t\right) dt$

$\quad=3e^t – 6(te^t-e^t)+C$

$\quad=9e^t -6te^t+C.$

#### Instructions

For this assignment all you’re going to do is *practice typing some *$\LaTeX$* code in the comments on this post.* Submit a comment using $\LaTeX$ on this post.

What you type doesn’t have to make any mathematical sense, just try to get it to compile some math symbols. Go ahead and play around and make a giant mess in these comments. If something doesnâ€™t work at first, donâ€™t worry just try again.Â

Instructions for typing in $\LaTeX$ on the OpenLab can be found here.

Two things to remember:

- Type ! at the top of your post/comment.
- Enclose your mathematical expression in dollar signs. (The instructions linked above use \ begin{math} and \ end{math} (without the spaces) instead of dollar signs, but you can use either to enclose your expression.)

[latexpage]

$\sum_{i=0}^{\infty} i^2$

$\int_0^{10} x^2 dx$

$\frac{\sqrt[3]{x}}{\cos(x^2)}$

\begin{equation}

\frac{d\heartsuit}{dt} > 0,

\frac{d^2\heartsuit}{dt^2} > 0,

\forall t > 0.

\end{equation}

$\frac{d\heartsuit}{dt} > 0,

\frac{d^2\heartsuit}{dt^2} > 0,

\forall t > 0.$

$\frac{d\heartsuit}{dt} > 0,$

$\frac{d\heartsuit}{dt} > 0,$

$\frac{d^2\heartsuit}{dt^2} > 0,$

$\forall t > 0.$

$\frac{\delta}{\delta x}[\frac{U(x)}{V(x)}] = \frac{U'(x)V(x) – U(x)V'(x)}{[V(x)]^2}$

$\lim_{x\to\infty} 3x^3+5x^2$

$e^{i/pi}+1=0$

$e^{\pi}+1$

$\lim_{n\to\infty}

$\lim_{n\to\infty}$

$\int\sec^2{(8x)}dx=\frac{1}{8}\tan(8x)+C$

\begin{math} \frac{x+10}{x^8 + 6x} \end{math}

$\sqrt[25]{11}$

\begin{math} \sqrt{2x+34} \end{math} + \begin{math} x^{85y} \end{math}

\begin{math} \sqrt{2x+76} \end{math}

\begin{math} \sqrt[5]{78xy} \end{math}

$\sqrt{x+2}$

$/sqrt{x+56}$ + $x^43$

$\sqrt{x+56}$ + $x^4$

\ begin{math}lint_1 linfty\!\frac{1}{x^2}\,dx=\left[-\frac{1}{x}\right]_11\infty-1\ end{math}

\begin{math} \sqrt{x+1} \end{math}

\begin{math} \sqrt{x=4} \end{math}

\begin{math} \sqrt{x+2} \end{math}

\ begin{math} sqrt{x}\end{math}

!

$ sqrt{x}$

!

\sqrt{x}

$

!

$\sqrt{x}$

\begin{math} \frac{x^16+x}{x^2 + 6x} + x \end{math}

\begin{math} \frac{2x^5+8}{x + 5x^17} \end{math}

!

\begin{math} \frac{x^2+17}{x + 14y^5} \end{math}

$\lim_{x\to\infty}$

$\frac{y^2-6}{y+3}$

.

\begin{math} x^{10y}\end{math}

\begin{math} \sqrt{5x+6x^2} \end{math}

!

$\begin{math} \sqrt{5x+2} \end{math}$

!

\begin{math}\sqrt[10]{59xy}\end{math}

!

\begin{math}x^{5y}\end{math}$

!

\begin{math}x^{78y}\end{math}$

!

$\begin{math}\sqrt[6]{22xy}\end{math}$

!

$\sqrt[7]{52xy}$

$\sqrt[4]{2x+7}$

!

\begin{math} \sqrt[4]{256x+16} \end{math}

!

$begin{math} \sqrt[4]{256x+16y} $end{math}

\begin{math} \c^2=a^2+b^2 \end{math} therefore \begin{math} \c=sqrt{a}+sqrt{b} \end{math}

$\c^2=a^2+b^2}$

$\c^2=a^2+b^2$

!

\sqrt{x-2}

$

/ sqrtx + 2