Find the limits on the table:
$$\begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill}} | c | c | c | c | c | c | c |}
\hline
2.9 & 2.99 & 2.999 & 3 & 3.001 & 3.01 & 3.1 \
\hline
-2 & 2 & -2 & 2 & -2 & 2 & -2 \
\hline
\end{tabular*}$$
$$\lim_{x \rightarrow 3} f(x)}$$

Question

Find the limits on the table:
$$\begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill}} | c | c | c | c | c | c | c |}
  \hline
  2.9 & 2.99 & 2.999 & 3 & 3.001 & 3.01 & 3.1 \
  \hline
  -2  & 2  & -2  & 2  & -2 & 2  & -2    \
  \hline
\end{tabular*}$$
$$\lim_{x \rightarrow 3} f(x)}$$

anonymous · Answer

http://mathurl.com/8nvrqd5 $$\lim_{x \rightarrow 3} f(x) = ?$$

anonymous · Answer

We don't know what $f(x)$ is?

anonymous · Answer

Limit as x approaches to three*

anonymous · Answer

Top row is x and bottom row is the function of x.

anonymous · Answer

We don't know anything about $f(x)$?  Not even if it is continuous or not?

anonymous · Answer

It seems like a oscillating behavor to me.

anonymous · Answer

If it is continuous then we know it is two.  Otherwise it's possible that it doesn't exist.

anonymous · Answer

But in both side, it approaches the same value, right? But if we keeping approaching, it still change from -2 to 2 to -2 to 2 and so on. It seems like we can't determined what it approaches to.

anonymous · Answer

So indeterminate?

anonymous · Answer

But if it touch three, it is two.

anonymous · Answer

We simply don't have enough information.  I could give you an example of functions which have the same result as the table, and yet have different limits.

anonymous · Answer

But if it is a continuous function, then we can be sure the limit is 2.

anonymous · Answer

Okay, I guess.

anonymous · Answer

You assume it is some oscillating function, but it could be piece wise!