% This is from another friend...

\title{Your title goes here\\
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\author{Your name goes here}


\documentclass{article}
\usepackage {amsfonts}
\usepackage {verbatim}
\begin {document}
\begin{center}

\maketitle

{\Large \LaTeX \,\,Worksheet 1}
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{\large Text Stuff}
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\end{center}

This paragraph is indented.

So is this one.

\noindent This one is {\bf not.}

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This one is also indented, but looks funny. \linebreak Why is that?

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{\it Example:} \,{\Huge Hi} {\huge Hi} {\LARGE Hi} {\Large Hi} {\large Hi} {\normalsize Hi} {\small Hi} {\footnotesize Hi} {\scriptsize Hi} {\tiny Hi}

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\noindent Here is a list of some things we've talked about so far:

\begin {enumerate}
\item[\bf (a)] Lists
\item[\bf (b)] Italics
\item[\bf (c)] Boldface
\end {enumerate}
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\noindent Here are some symbols you need to write with backslashes: \$, \#, \{\}, \%, \&.  And here are some left quotes: \lq\lq.

\pagebreak

\begin {center}
{\large Math Stuff}
\end {center}

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\noindent Here is some math embedded in text: $ax^2 + bx + c = 0.$  Here is more: $\sqrt[3]64 = 4.$
\\ Mathematicians love Greek letters like $\Omega$ and $\sigma.$  Sometimes we might have three 
\\ sigmas, $\sigma_1$, $\sigma_2$, and $\sigma_3.$ Maybe they're each squared: $\sigma_1^2$, $\sigma_2^2$, and $\sigma_3^2.$  Maybe we are rather intersecting sets A and B, obtaining $A \cap B.$  Here's an integral: $ \int_2^4 x {\mathrm d} x.$  
\\ Here's that integral in displaystye mode: $\displaystyle{\int _2^4 x \,\,{\mathrm d} x }.$

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\noindent Here is some displayed math:
$$ \int \frac{\sqrt{(ax+b)^3}}{x}{\mathrm d} x=\frac {2\sqrt{(ax+b)^3}}{3}+2b\sqrt{ax+b}+b^2 \int\frac{{\mathrm d} x}{x\sqrt{ax+b}}.$$

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\noindent This $$ 2(\frac{x}{y})$$ looks silly.  It is better to write: $$2\left( \frac{x}{y} \right).$$

\noindent You can also omit a large delimeter by using a period, as follows:$$\left. \frac{x^2}{2} \right]^6_2=18-2=16.$$

\noindent You do not need to do this to omit small delimteres: e.g., $x^2]_2^6=36-4=32.$

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\noindent Here is some math in an equation array, without number:

\begin {eqnarray*}
\lim_{x \to 0} \, \frac {{\mathrm {ln \, sin}} \,\pi x}{{\mathrm {ln\, sin}} \,x} &=& 
\lim_{x \to 0} \frac{ \pi \, \frac{{\mathrm {cos}} \,\pi x} {{\mathrm {sin}}\,\pi x}} 
{\frac {{\mathrm {cos}}\, x} {{\mathrm {sin}}\, x}} 
\\ &=& \lim_{x \to 0} \frac {\pi \, {\mathrm {tan}} \, x} {{\mathrm {tan}} \, \pi x}
\\&=& \lim_{x \to 0}\frac {\pi/{\mathrm{cos}}^2\, x}{\pi/{\mathrm{cos}} \, \pi x}
\\&=& \lim_{x \to 0} \frac{{\mathrm {cos}}^2\, \pi x}{{\mathrm{cos}}^2\, x}
\\&=& 1.
\end {eqnarray*}

\pagebreak

\noindent Notice how this equation array looks different:

\begin {eqnarray}
\lim_{x \to 0} \, \frac {{\mathrm {ln \, sin}} \,\pi x}{{\mathrm {ln\, sin}} \,x} &=& \lim_{x \to 0} \frac{ \pi \, \frac{{\mathrm {cos}} \,\pi x} {{\mathrm {sin}}\,\pi x}} {\frac {{\mathrm {cos}}\, x} {{\mathrm {sin}}\, x}} 
\\ \lim_{x \to 0} \frac {\pi \, {\mathrm {tan}} \, x} {{\mathrm {tan}} \, \pi x} &=& \lim_{x \to 0}\frac {\pi/{\mathrm{cos}}^2\, x}{\pi/{\mathrm{cos}} \, \pi x}
\\ \lim_{x \to 0} \frac{{\mathrm {cos}}^2\, \pi x}{{\mathrm{cos}}^2\, x} &=& 1.
\end {eqnarray}

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\begin {center}
{\large Packages}
\end {center}

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\noindent Here are some symbols I can make using the package amsfonts: $\mathbb {Z, \, R}.$

\begin {comment}
Here are some additional comments that aren't needed in the document.
\end {comment}

\end{document}