Question

Use the given graph to determine the limit, if it exists.

Answer 1

\[\lim_{x \rightarrow 3^{-}}\]

Answer 2

You are to determine the limit, if any exists, at which x=value?

Answer 3

3..?

Answer 4

@mathmale

Answer 5

ignore everything to the right of 3 on the x axis
to what y value is the line on the left headed?

Answer 6

Yes, x=3 is where the action is.

I see no fewer than three different vertical coordinates {1, 3, 7} struggling to be THE y-value. This is a sure sign that the function has no limit as you approach x=3 from the left AND from the right. As you come from the left towards x = 3, f(x) approaches but never touches y=1. As you come from the right towards x=3, following the solid line, y ou approach y=3 (actually, every point on that line has y=3). Is y=1 equal to y=3?

If no: This function does not have a limit at x=3; additionally, it's discontinuous at x=3.

If, on the other hand, you were to approach x=3 from the left on one graph and then approach x=3 from the right on the other graph, and you meet up at the same y-value at x=3, then you DO have a limit (even if the graph has a break at x=3).

Answer 7

"determine the limit, if it exists." Based upon the above info, can you now respond to this question?

Answer 8

it does not exist..?

Answer 9

look at the y coordinates of the ordered pairs for which the x-coordinate nearing 3 from the left are approaching...
for example what is (2.9,?) and (2.99,?) and (2.9999,?)
what are the ?'s getting closer to...
what happens if you block everything out to the right of x=3
and focus on what it is going on from the left of x=3 and fill in the dot from that direction and then ask yourself what is f(3) if that makes any sense