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\begin{enumerate}
\item What does it mean for the limit of $f(x)$ as $x$ approaches $0$ to be equal to $L$, or 
\[ \lim_{x \rightarrow 0} f(x) = L? \]
\item Consider the function $f(x) = \sin{\frac{1}{x}}$. Find a sequence of $x$'s that are positive, get closer and closer to zero, and have $f(x) = 1$. Hint: Think about for what values of $y$ we have $\sin{y} = 1$. For each of these $\frac{1}{y}$ will be an $x$ value that works for this problem. 
\item Find a similar sequence of $x$ values where $f(x) = -1$.
\item Find a similar sequence of $x$ values where $f(x) = 0$.
\item What does this mean for $\lim_{x \rightarrow 0} f(x) $? Think about what the definition of limit says.
\end{enumerate}

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