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\begin{center}
{\Large Warm-Up Problems

January 17, 2003}
\end{center}

\begin{enumerate}

\item  Find the following sums (practice with summation $\Sigma$ notation)
	\begin{enumerate}
	\item  \[ \sum_{i=1}^{5} (i^2+1) \]
	\item  \[ \sum_{j=4}^{6} \frac{j}{j+1} \]
	\item  \[ \sum_{i=1}^{n} (i+i^2) \]
	\end{enumerate}

\item  For the function $f(x)=1/x$, find an estimate for the area under the curve from $x=1$ to $x=3$ in the following ways:
	\begin{enumerate}
	\item  Using a left hand sum and 4 subintervals.
	\item  Using a right hand sum and 4 subintervals.
	\item  Using a mid-point rule and 4 subintervals.
	\item  Determine, if possible,(by looking at the graph) if your above estimates for the area are too large or too small.
	\end{enumerate}

\item  Using the following time-velocity data, find an estimate for the distance travelled in the time period from $t=0$ seconds to $t=6$ seconds.

\begin{tabular}{|c||c|c|c|c|c|}
\hline
\mbox{time (seconds)} & 0 & 2 & 4 & 6 \\
\hline
\mbox{Velocity (mph)} & 5.45 & 8.18 & 10.23 & 6.82 \\
\hline
\mbox{Velocity (ft/s)} & 8 & 12 & 15 & 10 \\
\hline
\end{tabular}

\end{enumerate}



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