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\begin{document}
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\begin{center} Quiz \#1A, MTH 1410
\end{center}
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Name: \underline{\hspace{3in}}


\begin{enumerate}

\item (4 points) For what value of $c$ is the function continuous at $x=4$? Make sure you explain your answer and use correct notation.

\begin{equation*}
f(x) =
\begin{cases}
\frac{x^2-5x+4}{x-4} & \text{if $x\neq 4$}\\
3c & \text{if $x= 4$}
\end{cases}
\end{equation*}

\newpage


\item (2 points) For the given graphs, calculate the limit or state that it does not exist.  If it does not exist, (briefly) explain why.
    
\vspace{2in}

(i) $\d{\lim_{x\to 1^+} [f(x)+g(x)]=}$

\vspace{1in}

(ii) $\d{\lim_{x\to 5^-} [f(x)\cdot g(x)]=}$

\vspace{1in}

\item (4 points) Calculate the limit, if it exists.  If it does not exist, explain why. Hint: Combine fractions, and be sure to use correct notation. $$\lim_{x\to 0}\frac{1}{x}\left(\frac{5}{7}-\frac{5}{x+7}\right)$$





\end{enumerate}
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