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+% Sample file: math.tex
+% Typeset with LaTeX format
+\documentclass{article}
+
+\begin{document} 
+In first year calculus, we   define intervals  such as 
+$(u, v)$ and $(u, \infty)$.  Such an interval is a 
+\emph{neighborhood} of  $a$
+if  $a$ is in the interval.  Students should 
+realize that  $\infty$ is only a
+symbol, not a number.  This is important since 
+we soon introduce concepts
+ such as $\lim_{x \to \infty} f(x)$.  
+
+When we introduce the derivative
+\[
+   \lim_{x \to a} \frac{f(x) - f(a)}{x - a},
+\]
+we assume that the function is defined and continuous 
+in a neighborhood of  $a$.
+\end{document}