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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Tue Apr 01 14:16:07 1997}
%TCIDATA{CSTFile=Math.cst}

\input{tcilatex}
\begin{document}


\section{CALCULUS, 6th Edition}

\section{and}

\section{CALCULUS OF A SINGLE VARIABLE, 2nd Edition}

\begin{center}
by Swokowski, Olinick, Pence

Notebooks by Cynthia E. Trimble, Ph.D.

Laurel Tutoring, San Carlos, California

Copyright(C) 1994 PWS Publishing Company
\end{center}

\subsection{Chapter 0 - Section A - Algebra, Part 1}

\subsubsection{Example 1}

Solve each equation

\begin{enumerate}
\item[(a)]  $x^{3}+3x^{2}-10x=0$
\end{enumerate}

The usual approach, as in the textbook, to solving this type of equation, is
to factor the expression. We can do this by selecting the left hand side of
the expression, holding down the Ctrl key, and choosing Maple Factor. The
result is

\begin{quotation}
$x\left( x+5\right) \left( x-2\right) =0$
\end{quotation}

From this, we can conclude that the solutions are $x=0$, $x=-5$, and $x=2$.
We can also find these solutions placing the insertion point anywhere within
the equation and using the Maple Solve Exact command to get

\begin{quotation}
Solution is : $\left\{ x=0\right\} ,\allowbreak \left\{ x=2\right\}
,\allowbreak \left\{ x=-5\right\} $
\end{quotation}

\begin{enumerate}
\item[(c)]  $7.3x^{2}-31.7x+15.2=0$
\end{enumerate}

Using Solve Exact or Solve Numeric on this equation yields

\begin{quotation}
Solution is : $\left\{ x=3.\,7936\right\} ,\allowbreak \left\{
x=.\,54887\right\} $
\end{quotation}

When an expression contains numbers with decimal points, Maple always finds
the solution numerically. To obtain an exact solution, first write the
equation in equivalent ``exact'' form using rational numbers:

$\frac{73}{10}x^{2}-\frac{317}{10}x+\frac{152}{10}=0$

Placing the insertion point in this form of the equation and choosing Solve
Exact yields

\begin{quotation}
Solution is : $\left\{ x=\frac{317}{146}+\frac{7}{146}\sqrt{1145}\right\}
,\allowbreak \left\{ x=\frac{317}{146}-\frac{7}{146}\sqrt{1145}\right\} $
\end{quotation}

We can also use the graphing features of Scientific Notebook to find the
solution. Place the insertion point in the left-hand side of the equation
and choose Maple Plot 2D Rectangular.

$7.3x^{2}-31.7x+15.2=0$

\begin{center}
\FRAME{itbpF}{3in}{2in}{0in}{}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 3in;height 2in;depth 0in;display "USEDEF";function
\TEXUX{$7.3x^{2}-31.7x+15.2$};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";xmin "-5";xmax "5";xviewmin "-5.2";xviewmax
"5.204";yviewmin "-26.66";yviewmax "363.9";phi 45;theta 45;plottype
4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}
\end{center}

The solutions of our equation are where the graph crosses the x-axis; they
are also known as the roots.

Depending on the expression you plot, you may need to change the range or
zoom in or out to see where the graph crosses the x-axis. Our guess from the
graph, without looking at the solutions we found above, is that the first
solution is near $x=0.5$, and the second is near $x=3.8$.

To come up with more exact answers from the graph, you can zoom in very
close to the points where the function crosses the axis. Double click the
graph, click the zoom tool (the close mountain), then click and drag a small
region that includes one of the points where the graph crosses the x axis.

\begin{center}
\FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"USEDEF";function \TEXUX{$7.3x^{2}-31.7x+15.2$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "0.21897";xmax "0.70073";xviewmin
"0.219";xviewmax "0.7007";yviewmin "-3.669";yviewmax "8.854";rangeset"X";phi
45;theta 45;plottype 4;numpoints 49;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}}
\end{center}

Continue clicking and dragging a small part of the plot where the line
crosses the x axis.

\begin{center}
\FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"USEDEF";function \TEXUX{$7.3x^{2}-31.7x+15.2$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "0.54771934";xmax
"0.54944884";xviewmin "0.5477";xviewmax "0.5494";yviewmin
"-0.01452";yviewmax "0.02811";rangeset"X";phi 45;theta 45;plottype
4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}
\end{center}

\subsubsection{Comparing the Methods}

What's the difference between the methods we used above? When should we use
each of the methods? First of all, quadratic equations are special - exact
solutions can always be found. But factoring may not always work, especially
when the equations are beyond quartic (i.e., fourth power). That is when you
should use the Solve Numeric command.

\end{document}
