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For each of the following functions and values $x=a$:
\begin{enumerate}[(a)]
    \item If you were to directly plug in $x=a$ to this function, what would the value look like? Your answer should be one of \[ \frac{0}{0} \qquad 0^0 \qquad 1^\infty \] These are all examples of \textit{indeterminate forms.}
    \item Draw a graph of the function near $x=a$. Using this or a table of values, compute \[ \lim_{x\rightarrow a^-} \qquad \lim_{x\rightarrow a^+} \qquad \lim_{x\rightarrow a} \] for this function. 
\end{enumerate}

\begin{enumerate}[1.]
    \item $\displaystyle f(x) = \frac{x^2 - 4}{x-2} \qquad x=2$
    \item $\displaystyle g(x) = \frac{x^2 - 9}{x^2-6x+9} \qquad x=3$
    \item $\displaystyle h(x) = \frac{x^2 + 2x + 1}{x+1} \qquad x=-1$
    \item $\displaystyle l(x) = \frac{\sin{x}}{x} \quad x=0$
    \item $\displaystyle m(x) = x^{\sin{x}} \qquad x=0$
    \item $\displaystyle n(x) = x^{(1/\ln(2x)}\qquad x=0$
    \item $\displaystyle q(x) = (1+\ln(x))^{1/(x-1)} \qquad x=1$
    \item $\displaystyle r(x) = (\cos{x})^{3/x^2} \qquad x=0$
    \item $\displaystyle s(x) = \left(1 + x\right)^{\frac{1}{x}} \qquad x=0$
\end{enumerate}
\begin{enumerate}
    \item[(c)] What can you say about limits of the form $\frac{0}{0}$, $0^0$ or $1^\infty$?
\end{enumerate}

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