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\makeatletter


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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{Trigonometric functions}


\subsubsection{Limits of trig functions}

\begin{xca}
\[
\displaystyle \lim _{x\rightarrow 0}\frac{\sin (3x)}{\sin (4x)}=\]

\end{xca}

\subsubsection*{Hint:}

\begin{eqnarray*}
\frac{\sin (3x)}{\sin (4x)} & = & \frac{\sin (3x)}{1}\frac{1}{\sin (4x)}\\
 & = & \frac{3}{4}\frac{\sin (3x)}{3x}\frac{4x}{\sin (4x)}.
\end{eqnarray*}

\end{document}
