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\begin{center}\begin{Large} Integrals, Sums, and Limits\\
\end{Large}            A sample LaTeX file\\
Matchett, \today
\end{center}
Here are some examples of integrals.
\begin{displaymath}
\int 2x + 3x^2 dx  = x^2 + x^3 + c
\end{displaymath}
If you want to tinker with the exact spacing of the items that make up an 
integral, use the math space symbols:
\begin{verbatim}
  \, tiny space     \: medium space     \; big space    
  \  bigger space   \quad   still bigger space          
  \qquad   biggest space of all
  \! tiny negative space
\end{verbatim}
Using some of these changes the above equation to
\begin{displaymath}
\int 2x + 3x^2\,dx \ = \ x^2 + x^3 + c
\end{displaymath}
Definite integrals are not much harder.
\begin{displaymath} 
\int_{0}^{\pi/2} \cos x \, dx \ = \ \sin x\big|_0^{\pi/2}
= \sin(\pi/2) - \sin(0) = \framebox{1}
\end{displaymath}
 
Summations are done as follows.
\begin{displaymath}
\sum_{n=1}^4 n^2 = 1 + 4 + 9 + 16
\end{displaymath}
And limits are prettly simple, too.
\begin{displaymath}
  \lim_{h \rightarrow 0} \frac{\sin h}{h} = 1
\end{displaymath}

The equationarray environment is great for working through several steps of 
calculations:
\begin{eqnarray*}  
\int_1^2 3x^2 dx & = & x^3\Big|_1^2  \\
    & = & 8 - 1 \\
   & = & 7
\end{eqnarray*}
Use ``eqnarray'' without the asterisk if you want the lines numbered.  In that 
environment, the line number can be suppressed by including  ``nonumber'' on 
the line in question.

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