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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Mar 27 14:52:47 1997}
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\begin{document}


\subsection{Evaluate and Evaluate Numerically\label{Evaluate}\hrulefill}

Collecting terms, finding the sum or difference of polynomials, changing a
quotient to rational form, and raising a number to a power are easily
accomplished with the Evaluate and Evaluate Numerically commands. When you
evaluate an expression\textit{,} Maple returns an exact or symbolic answer
whenever appropriate and a numerical approximation otherwise. You can use
the Evaluate Numerically command to force a numerical result for any
evaluation. These examples illustrate how to evaluate expressions.

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}\textit{%
Evaluate }$\protect\sqrt{2.36}$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{}{radical.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 19.8125pt;height 18.9375pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'Radical.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Radical. \textit{Scientific
Notebook} starts mathematics automatically.

\item  Type \textbf{2.36}. Your screen shows the expression $\sqrt{2.36}.$

\item  Click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{eval.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
20.3125pt;original-height 18.8125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'eval.wmf';file-properties "XNPEU";}}or, from
the Maple menu, choose Evaluate. Maple evaluates and you see this: $\sqrt{%
2.36}=\allowbreak 1.\,5362.$
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}\textit{%
Evaluate} $\left( 0.16\right) ^{-1}$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{19.8125pt}{18.9375pt}{2pt}{}{}{parens.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 19.8125pt;height 18.9375pt;depth
2pt;original-width 20.3125pt;original-height 20.3125pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'parens.wmf';file-properties
"XNPEU";}}, type \textbf{0.16,} and press spacebar.

\item  Click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{supscrip.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'supscrip.wmf';file-properties "XNPEU";}}or,
from the Insert menu, choose Superscript. Type \textbf{-1}. Your screen
shows the expression $\left( 0.16\right) ^{-1}$.

\item  Click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{eval.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
20.3125pt;original-height 18.8125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'eval.wmf';file-properties "XNPEU";}}or, from
the Maple menu, choose Evaluate. Maple evaluates the expression and displays
the result $6.25$ on your screen.
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}\textit{%
Evaluate Numerically} $936\div 14$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics.

\item  Type \textbf{936,} click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{%
divide.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 22.4375pt;height 21.0625pt;depth
2pt;original-width 20.3125pt;original-height 18.8125pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'divide.wmf';file-properties
"XNPEU";}}, and type \textbf{14.}

\item  Click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{evalnum.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
20.3125pt;original-height 18.8125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'evalnum.wmf';file-properties "XNPEU";}}or, from
the Maple menu, choose Evaluate Numerically. Your screen displays the result 
$\allowbreak 66.\,\allowbreak 857$ on your screen.
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}\textit{%
Evaluate Numerically} $\pi $}

\begin{enumerate}
\item  Click\FRAME{itbpF}{21.125pt}{20.5pt}{2pt}{}{}{pi.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 21.125pt;height 20.5pt;depth
2pt;original-width 19.5625pt;original-height 18.8125pt;cropleft "0";croptop
"1.0079";cropright "1.0025";cropbottom "0";filename 'pi.wmf';file-properties
"XNPEUR";}}and click \FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{evalnum.wmf%
}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 22.4375pt;height 21.0625pt;depth
2pt;original-width 20.3125pt;original-height 18.8125pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'evalnum.wmf';file-properties
"XNPEU";}}or, from the Maple menu, choose Evaluate Numerically. The
evaluation yields this result: \ $\pi =\allowbreak 3.\,1416.$\medskip 

\item  Now see how\ the results differ when you change the numerical
accuracy with which Maple operates:

\begin{enumerate}
\item  From the Maple menu, choose Settings.

\item  Choose \ the General tab.

\item  Change the setting for Digits Used in Computations to 50.

\item  Change the setting for Digits Used in Display to 50 and choose OK.

\item  Press Enter, click\FRAME{itbpF}{21.125pt}{20.5pt}{2pt}{}{}{pi.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 21.125pt;height 20.5pt;depth
2pt;original-width 19.5625pt;original-height 18.8125pt;cropleft "0";croptop
"1.0079";cropright "1.0025";cropbottom "0";filename 'pi.wmf';file-properties
"XNPEUR";}}, and then click \FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{%
evalnum.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 22.4375pt;height 21.0625pt;depth
2pt;original-width 20.3125pt;original-height 18.8125pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'evalnum.wmf';file-properties
"XNPEU";}}or, from the Maple menu, choose Evaluate Numerically. Your screen
now shows this value for $\pi $: \medskip 
\end{enumerate}
\end{enumerate}

\begin{center}
\[
\fbox{%
\begin{tabular}{lll}
\rule[-0.1in]{0in}{0.3in} & $\pi =\allowbreak
3.\,14159\,26535\,89793\,23846\,26433\,83279\,50288\,41971\,69399\,3751$ & 
\rule[-0.1in]{0in}{0.3in}%
\end{tabular}
} 
\]
\medskip
\end{center}

Return to the original settings unless you routinely need this degree of
accuracy.

\subparagraph{\textit{Evaluate these expressions}$\protect\medskip $\label%
{exercises}}

\begin{quotation}
$\rule[-0.12in]{0in}{0.3in}$\qquad Compute these expressions with Evaluate: 
\[
27+33-16\text{\hspace{0.5in}}14.2\times 83.5\text{\hspace{0.5in}}\left|
-11.3\right| \text{\hspace{0.5in}}\left( 3x^{2}+3x\right) +\left(
8x^{2}+7\right) 
\]

\qquad Compute these expressions with Evaluate Numerically:

\[
\frac{8}{9}\text{\hspace{0.5in}}\sqrt{2}\text{\hspace{0.5in}}%
\int_{0}^{1}e^{x^{2}}dx 
\]

\qquad Compute these expressions with Evaluate and Evaluate Numerically,
noting the different results:

\[
\rule[-0.22in]{0in}{0.45in}\dfrac{-\frac{2}{3}}{\frac{8}{7}}\text{\hspace{%
0.5in}}\int xdx=\frac{1}{2}x^{2}\text{\hspace{0.5in}}\frac{5}{8}\times \frac{%
1}{7}\text{\hspace{0.5in}}\left( x+3\right) +\left( x-y\right) \text{\hspace{%
0.5in}}4^{-3} 
\]
\end{quotation}

\end{document}
