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\author{Doug Hundley}
\title{Calc Lab 1:  Parametric Curves and Arc Length}

\begin{document}
\maketitle


\begin{center}
{\bf Due Date:  With the rest of Lab 1- at the beginning of class on 9/23
or 9/24 (See the schedule)}
\end{center}

\bigskip

The purpose of this lab is to continue getting you familiar with LaTeX,
and start working on some mathematics.  Note that the full ``Lab 1'' will
be the homework from last week, this sheet, plus some extra stuff
next week.  For this week,
write your solution using the template on our class webpage 
(\verb+template.tex+).


\section{The Question}
\label{QuestionSect}

A certain curve is defined parametrically, $(x(t), y(t))$ as:
\begin{equation}
x(t)=\int_1^t \frac{\cos(u)}{u}\,du \qquad 
y(t)=\int_1^t \frac{\sin(u)}{u}\,du
\label{Defn01}
\end{equation}
Find the length of the arc of the curve from the origin to the nearest
point where there is a vertical tangent line using Equation \ref{Defn01}.
You may use a Calculus
text (for example, \cite{Calc1})
to help you, but  be sure to write out a full solution.

\section{Group Work}
We'll be working in groups- You might try to divide up the workload; for
example, have someone look up the appropriate mathematics, and
have someone else start the LaTeX write up, etc.  This sentence shows
you how to reference a previous section, like Section \ref{QuestionSect}.


\section{Guidelines for grading:}

These are the things I will be looking for when I am grading
this part of your Lab:
\begin{enumerate}
\item The problem and final answer are clearly stated.
\item The mathematics are nicely typeset, including the
use of whitespace (for example, \verb+\quad+, \verb+\qquad+, \verb+\,+
where necessary)
\item LaTeX issues I will focus on:
\begin{itemize}
\item Use a title and section headings.
\item Be able to use sizable parentheses.
\item Be able to label and number an equation and refer
to it in the text (not manually, but by using LaTeX commands).
\end{itemize}
\item Use the Hints Sheet, Page 1 (see the class website)
\end{enumerate}

\begin{thebibliography}{99}
\bibitem{Calc1} Stewart, J. 2003, {\it Calculus}, 5th edition,
Brooks-Cole.
\end{thebibliography}


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