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

March 21, 2003}
\end{center}

\begin{enumerate}

\item  As you come in, please tell me your height in inches.

\item  Consider the function $f(t)=A e^{-ct}$ for $t \geq 0$ where $A$ and $c$ are constants.
	\begin{enumerate}
	\item  Suppose you want to ensure $\int_{0}^{\infty} f(t)\; dt =1$.  Find conditions on $A$ and $c$ to ensure this.
\bigskip

	\item  Suppose, in addition, you know that $A=0.01$, what is $c$?
\bigskip

	\item  Using your $A=0.01$ and the $c$ that you just found, find a nice expression for the function:
		\[
		F(t) = \int_0^{t} f(u) \; du
		\]
\bigskip

	\item  What is $\lim_{t \ra \infty} F(t)$?
\bigskip

	\item  Compute: $\int_0^\infty tf(t)\; dt$.

	\end{enumerate}

	
\end{enumerate}

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