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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 3}\quad {\sl Sept. 22, 1994}

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

  \begin{enumerate}[a)]
  \item A partition of $[a,b]$.
  \answerspace

  \item A step function 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
\problemspace
\item State precisely the following theorems about integrals of step
functions.
  \begin{enumerate}
  [a)] \item Linearity Property.
  \answerspace

  \item Invariance Under Translation.
  \answerspace
  \end{enumerate}

\problemspace
\item Compute $\int_{-2}^4 3[x] + [x/4]\,dx$.
\answerspace
\end{enumerate}

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