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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 3}\quad {\sl Sept. 17, 1998}

\begin{enumerate}
\problemspace
\item Define the following:

  \begin{enumerate}[a)]
%  \item A partition of $[a,b]$.
%  \answerspace
  \item A step function $s$ on $[a,b]$.
  \answerspace
  \item $\int_a^b s(x)\,dx$ where $s$ is a step function on $[a,b]$.
  \answerspace
  \item $\int_a^b f(x)\,dx$ where $f$ is a bounded function on $[a,b]$.
  \answerspace
  \end{enumerate}

%\newpage
%\item Let $s$ and $t$ be step functions such that
%$\int_{-2}^3 s(x)\,dx = -1$ and \mbox{$\int_0^1 t(x)\,dx = 2$}.
%Determine the value of $\int_{0}^5 4s(x-2) + t(x/5)\,dx$. (Justify your
%steps).

%\vfil

\problemspace
\item State and prove the Linearity Property for integrals of step
functions.

\answerspace
\end{enumerate}

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