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%TCIDATA{<META NAME="Title" CONTENT="Calculus">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:05:16 1997}
%TCIDATA{Language=American English}
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%TCIDATA{<LINK REL="author" HREF="DM0-1.tex">}
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\begin{document}


\section{Calculus\label{Calculus expressions}}

In this chapter, we treat the standard topics from differential and integral
calculus, including limits, sequences, and series. The notion of a function
is fundamental to the study of calculus. In this chapter we assume that you
have read and understand how to define and manipulate functions in \textsl{%
Scientific Notebook}. Functions were introduced in the chapter \hyperref{%
Algebra}{}{}{DM3.tex}, with a description of procedures for naming
expression and functions. Basic information on working with functions and
expressions is summarized in the chapter on \hyperref{Functions and
Definitions}{}{}{DM5.tex}, along with additional information on storing and
retrieving definitions. We give several examples in this chapter that
illustrate connections between calculus and the function plots introduced in
the chapter \hyperref{Plotting Curves and Surfaces}{}{}{DM6.tex}.

\subsection{\ Evaluating Calculus Expressions\label%
{Evaluating calculus expressions}}

You can evaluate calculus expressions with \textsl{Scientific Notebook} in
the same manner as expressions from algebra or trigonometry.

\begin{quote}
$\blacktriangleright $ To calculate a derivative or an integral
\end{quote}

\begin{enumerate}
\item[1.]  Enter the derivative or integral using standard mathematical
notation.

\item[2.]  Leave the insertion point in the expression.

\item[3.]  From the \textsf{Maple} menu, choose \textsf{Evaluate}; or click 
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{evaluate.wmf}{\special%
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\end{enumerate}

\strut

\begin{example}
Carry out the following steps to calculate the integral $\int_{0}^{\pi
}x\sin x\,dx.$

\begin{enumerate}
\item  Enter the expression $\int_{0}^{\pi }x\sin x\,dx$, using the keyboard
and appropriate icons at the top of the screen. (Click \FRAME{itbpF}{0.3009in%
}{0.3009in}{0.0701in}{}{}{subscrip.wmf}{\special{language "Scientific
Word";type "GRAPHIC";display "PICT";valid_file "F";width 0.3009in;height
0.3009in;depth 0.0701in;original-width 17.8125pt;original-height
16.9375pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Subscrip.wmf';file-properties "XNPEU";}} for a subscript box for the lower
limit, press \textsc{tab} to take the insertion point to a superscript
position for the upper limit, and press \textsc{spacebar} to put the
insertion point back in line.)

\item  Leave the insertion point in the expression $\int_{0}^{\pi }x\sin
x\,dx$ and, from the \textsf{Maple} menu, choose \textsf{Evaluate}; or click 
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{evaluate.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
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\end{enumerate}
\end{example}

\begin{quote}
$\blacktriangleright $ Evaluate
\end{quote}

\begin{quotation}
$\dint_{0}^{\pi }x\sin x\,dx=\allowbreak \pi $
\end{quotation}

\strut

\textsf{Note}: Compare the area bounded by the red figure and the area of
the rectangle bounded by the blue and red lines.

\FRAME{dtbpFU}{3in}{2.0003in}{0pt}{\Qcb{$y=x\sin x$, $y=1$}}{}{}{%
\special{language "Scientific Word";type "MAPLEPLOT";width 3in;height
2.0003in;depth 0pt;display "PICT";function \TEXUX{$x\sin x\,$};linecolor
"red";linestyle 1;linethickness 2;pointstyle "point";function
\TEXUX{$(0,1,3.14159,1,3.14159,0)$};linecolor "blue";linestyle
1;linethickness 2;pointstyle "point";function
\TEXUX{$(0,0,3.14159,0)$};linecolor "red";linestyle 1;linethickness
3;pointstyle "point";function \TEXUX{$(0,0,0,1)$};linecolor "blue";linestyle
1;linethickness 2;pointstyle "point";xmin "0";xmax "3.14159";xviewmin
"-0.06283";xviewmax "3.206";yviewmin "-0.03639";yviewmax
"1.857";rangeset"X";phi 45;theta 45;plottype 4;plotticks 1;num-x-ticks
3;num-y-ticks 2;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}

\strut

\subsection{\ Related topics}

\begin{itemize}
\item  \hyperref{Selecting Mathematical Expressions}{}{}{DM1-3.tex#Selecting
an expression}

\item  \hyperref{Limits}{}{}{DM7-2.tex#Limit}

\item  \hyperref{Differentiation}{}{}{DM7-3.tex#Derivative}

\item  \hyperref{Evaluating Indefinite Integrals}{}{}{DM7-4.tex#Indefinite
integral}

\item  \hyperref{Exercises and Solutions}{}{}{DM7-9.tex#Exercises}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{0.5275in}{0.3399in}{0.0519in}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
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"1";cropbottom "0";filename 'index.wmf';file-properties "XNPEU";}}}{}{}{%
DMIndex.tex#Math Index}\quad {\small Index entries: \hyperref{Evaluate}{}{}{%
DMIndex.tex#Evaluate}, \hyperref{Selecting mathematical expressions}{}{}{%
DMIndex.tex#Selecting mathematical expressions}}

\end{document}
