%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="31">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="Title" CONTENT="Combine">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Wed Mar 26 17:24:52 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=booklet.cst}
%TCIDATA{PageSetup=61,61,114,114,1}
%TCIDATA{<LINK REL="author" HREF="GSfront.tex">}
%TCIDATA{<LINK REL="first" HREF="GSCompute.tex">}
%TCIDATA{<LINK REL="contents" HREF="GScontents.tex">}
%TCIDATA{<LINK REL="copyright" HREF="GSfront.tex">}
%TCIDATA{<LINK REL="end" HREF="GSCompute15.tex">}
%TCIDATA{<LINK REL="index" HREF="GSindex.tex">}
%TCIDATA{<LINK REL="next" HREF="GSCompute4.tex">}
%TCIDATA{<LINK REL="parent" HREF="GSCompute.tex">}
%TCIDATA{<LINK REL="previous" HREF="GSCompute2.tex">}
%TCIDATA{<LINK REL="publisher" HREF="GSfront.tex">}
%TCIDATA{<LINK REL="top" HREF="GScontents.tex">}
%TCIDATA{<LINK REL="trademark" HREF="GSfront.tex">}
%TCIDATA{AllPages=
%H=78,\PARA{038<p type="texpara" tag="Body Text" >\hfill Getting Started with Scientific Notebook}
%F=36
%}


\input{tcilatex}
\begin{document}


\subsection{Combine\label{Combine}\hrulefill}

In addition to combining the terms in mathematical expressions, you can use
the Combine command to demonstrate the laws of exponents and the properties
of logarithms.

\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{%
Combine \texttt{sin\textit{\thinspace }}}$x$\textit{\texttt{\textit{%
\thinspace }cos\textit{\thinspace }\thinspace }}$y+$\textit{\texttt{%
\thinspace \textit{\textit{\thinspace }}cos\textit{\textit{\thinspace }}%
\thinspace }}$x$\textit{\texttt{\textit{\thinspace }sin\thinspace }}$y$}

\noindent You don't need to type any spaces as you enter the functions. 
\textit{Scientific Notebook} interprets the trigonometric functions and
formats the expression correctly, displaying the function names in gray.

\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{sinxcosy}. Your screen shows the expression $\sin x\cos y
$.

\item  Type \textbf{+cosxsiny}. On your screen, you see $\sin x\cos y+\cos
x\sin y$

\item  From the Maple menu, choose Combine and then choose Trig Functions.

Your result is: \ $\sin x\cos y+\cos x\sin y=\allowbreak \sin \left(
x+y\right) .$\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{%
Combine the powers of \thinspace }$10^{x}10^{y}$\textit{\ }}

\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{10 }, press \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{x, }%
and then press spacebar.

\item  Type \textbf{10 }, press \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";}}, and type \textbf{y}.

\item  From the Maple menu, choose Combine and then choose Powers. After the
calculation is complete, your screen shows this: $10^{x}10^{y}=\allowbreak
10^{x+y}$.\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{%
Combine \ \texttt{log\textit{\thinspace }}}$x+$\texttt{log}\textit{\texttt{%
\textit{\thinspace }}}$y$}

\noindent Note that \textit{Scientific Notebook} automatically interprets%
\textit{\ log }as a function, displaying it in a different color on your
screen.

\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{logx+logy}.

\item  From the Maple menu, choose Combine and then choose Logs. This is
your result: $\log x+\log y=\allowbreak \ln \left( x\unit{y}\right)
.\medskip $
\end{enumerate}

\subparagraph{\textit{Combine the terms in these expressions\protect\medskip 
\label{exercises}}}

\begin{quotation}
\[
\left( e^{x}\right) ^{y}\text{\hspace{0.5in}}3\ln x\text{\hspace{0.5in}}\sin
x\sin y\text{\hspace{0.5in}}\left( 2^{x}\right) ^{y} 
\]
\end{quotation}

\end{document}
