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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{Computing limits}

\begin{example}
Compute \[
\lim _{x\rightarrow 3}\frac{x^{2}-x-6}{x^{3}-4x^{2}+3x}.\]

\end{example}

\subsubsection*{Hints}

For this, we note first that when \( x=3, \) both the numerator and the denominator
are 0. This is, as mentioned earlier, a signal that you have to do more. What
can you do to make sense of that limit? Certainly 0/0 is not a good answer.


\subsubsection*{Another hint}

The key to making sense of the 0/0 in this limit is to factor both the numerator
and denominator. That may seem hard, but remember that both the numerator and
the denominator are 0 when \( x=3 \), so \( (x-3) \) is a factor of both:\[
\frac{x^{2}-x-6}{x^{3}-4x^{2}+3x}=\frac{(x-3)()}{(x-3)()}.\]



\subsubsection*{Still stuck?}
\end{document}
