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%TCIDATA{<META NAME="Title" CONTENT="Check Equality">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Wed May 14 11:35:43 1997}
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\input{tcilatex}
\begin{document}


\subsection{Check Equality\label{Check Equality}\hrulefill}

In \textit{Scientific Notebook,} you can determine whether an equality is
true or false or whether, if the test is inconclusive, the inequality may be
either true or false.

\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{%
Check the equality } $1+1=3$}

\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{1+1=3.}

\item  From the Maple menu, choose Check Equality. You see this result: \ $%
1+1=3$ is false.\medskip 
\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{%
Check the equality } $\frac{9}{8}-\frac{8}{9}=\left| \frac{9}{8}-\frac{8}{9}%
\right| $}

\begin{enumerate}
\item  Click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{fraction.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 'fraction.wmf';file-properties "XNPEU";}}or,
from the Insert menu, choose Fraction. Type \textbf{9}, press Tab, type 
\textbf{8}, and press spacebar.

\item  Type \textbf{- }, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{%
fraction.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 'fraction.wmf';file-properties
"XNPEU";}}, type \textbf{8}, press Tab, type \textbf{9}, and press spacebar.

\item  Type \textbf{= }, click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{%
brackets1.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 'brackets1.wmf';file-properties
"XNPEU";}}, choose\FRAME{itbpF}{19.5625pt}{33.125pt}{2pt}{}{}{Figure }{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 19.5625pt;height 33.125pt;depth
2pt;original-width 19.5625pt;original-height 34.625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'absolute.wmf';file-properties
"XNPEU";}}, and choose OK.

\item  Type the two fractions again.

\item  From the Maple menu, choose Check Equality. On your screen, you see
this result: $\dfrac{9}{8}-\dfrac{8}{9}=\left| \dfrac{9}{8}-\dfrac{8}{9}%
\right| $ is true.\medskip 
\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{%
Check the equality \ \texttt{arcsin}}$\left( \text{\texttt{sin}}\mathit{%
\mathtt{\mathit{\,}}}x\right) =x$}

\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 the function \textbf{arcsin} . \textit{Scientific Notebook}
recognizes the function and displays it in gray on your screen.

\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{sinx}, press spacebar, and type \textbf{=x}. The
program recognizes and properly displays the function.

\item  From the Maple menu, choose Check Equality. Maple cannot determine
whether the equality is true or false and displays this result: $\arcsin
\left( \sin x\right) =x$ is undecidable.\medskip 
\end{enumerate}

\subparagraph{Check these equalities\protect\medskip \textit{\label%
{exercises}}}

\begin{quotation}
\[
e^{i\pi }=-1\text{\hspace{0.5in}}\pi =3.14\text{\hspace{0.5in}}\sin
^{2}x+\cos ^{2}x=1\medskip 
\]
\end{quotation}

\end{document}
