\documentclass[11pt]{article}
\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
\usepackage{latexsym,amsmath,amssymb,epsfig}
\setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\textheight}{8.0in}
\begin{document}
\centerline{MATH 133 -- Calculus with Fundamentals 1}
\centerline{Quiz 3 -- October 1, 2015}
\vskip 10pt
\noindent
Your Name: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\vskip 10pt
\noindent
{\it Directions}
\vskip 10pt
Do all work in the spaces provided below and on the back.  There are 30 total points possible.  You may use a calculator (but not any graphing features).  
\vskip 10pt
\noindent
{\it Questions}
\vskip 10pt
\begin{enumerate}
\item[1)]  An object moves along a straight line path with position given by $x(t) = 2t^2 - t + 4$ 
($t$ in seconds, $x$ in feet).   
\begin{enumerate}
\item[(a)] (5)  What is the average velocity of the object over the interval $[1,4]$ of $t$-values?
\vglue 3truein
\item[(b)] (5)  The following table gives average velocities computed over the indicated intervals.  Using
this information, estimate the \emph{instantaneous velocity} at $t = 1$.  
$$\begin{array}{ccccccccc}
\hline
{\rm interval} &\vline& [1,1.5] &\vline& [1,1.05] &\vline& [1,1.005] &\vline& [1,1.0005]\\ \hline
{\rm ave. vel.}&\vline&  4      &\vline&    3.1   &\vline&    3.01   &\vline&  3.001   \\ \hline 
\end{array}$$
\vskip 10pt
Instantaneous velocity:
\end{enumerate}
\vfill\eject
\item[2)] (10)  Complete the following table and use your results to determine an estimate of the limit 
$\displaystyle{\lim_{x\to 2} \frac{x - 2}{x^2 - 3x + 2}}$.  Use at least 5 decimal places in all calculations for these.
$$\begin{array}{cccccccccccccc}
\hline
x                       &\vline& 2.1 \qquad &\vline& 2.01\qquad &\vline& 2.001\qquad &\vline& 1.999\qquad &\vline& 1.99\quad\qquad &\vline& 1.9\qquad\qquad  \\ \hline
\displaystyle{\frac{x-2}{x^2 - 3x + 2}} &\vline&        &\vline&      &\vline&       &\vline&       &\vline&      &\vline&     \\ \hline 
\end{array}$$
\vglue 5truein
$\displaystyle{\lim_{x\to 2} \frac{x - 2}{x^2 - 3x + 2}} \doteq \underline{\qquad\qquad\qquad}$
\vfill\eject
\item[3)] Refer to the graph in Figure 1 and fill in the answers to these questions.
\begin{enumerate}
\item[(a)] (5) From the graph,  $\displaystyle{\lim_{x \to 1} f(x)} = \underline{\qquad\qquad\qquad}$.
\item[(b)] (5) From the graph,  $\displaystyle{\lim_{x \to 3^+} f(x)} = \underline{\qquad\qquad\qquad}$ and 
$\displaystyle{\lim_{x\to 3^-} f(x)} = \underline{\qquad\qquad\qquad}$.
Does $\lim_{x \to 3} f(x)$ exist?  $\underline{\qquad\qquad\qquad}$
\begin{figure}
\begin{center}
\includegraphics[width=.5\linewidth]{Q3G.png}
\caption{Figure for Question 3}
\end{center}
\end{figure}

\end{enumerate}
\end{enumerate}
\end{document}
