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\textbf{Math 165: Honors Calculus I}

\textbf{Topics for Final Exam} \quad
\textsl{PCTR 102 8:00--10:00 A.M., Dec. 15, 1998}


\bigskip
The following list is an overview of the topics that may be covered on
the final exam. When a topic is listed, all the definitions and named
theorems associated with that topic are implied, although in some cases
these have been separately emphasized.

\begin{itemize}

\item The natural numbers, induction

\item Summation, the binomial theorem

\item Partitions and step functions, integrals of step functions

\item Supremum and infimum

\item Definition of the integral

\item Theorems about integrals

\item Area and average

\item Trig functions and identities

\item Limits, one-sided limits, theorems about limits

\item Continuity

\item Balzano's Theorem and the Intermediate Value Theorem 

\item Inverse functions and their properties

\item Mean Value Theorem for Integrals

\item Derivative and their properties

\item Power rule, higher derivatives, the chain rule

\item Tangent lines

\item Implicit derivatives

\item Related rates

\item Extreme values of differentiable functions

\item Mean Value Theorem for Derivatives

\item First and Second Derivative Tests for Extrema

\item Convexity

\end{itemize}

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