Help with limits for a medal?

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Help with limits for a medal?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Use the graph to find the limit and determine the continuity of the function.
Sorry about that. My internet is giving me some troubles.
What limit?
np the servers here are funny sometimes.
Just a sec. It's not letting me post them
Hah! Got it!
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Right, this is what I figured. Ok as you walk along the graph from left to right there is an obvious problem at \(x=-1\). What value do you approach(y value) as you get closer to \(x=-1\)
There's a hole in the graph
what value is y when you approach from the left?
2
so \(\lim_{x\rightarrow c^{-}}f(x)=2\) What about from the right?
It gets closer to 0
Yep so \(\lim_{x\rightarrow 2^{+}}f(x)=0\)
now does \(2\ne 0\)?
Yes, 2 doesn't equal zero.
obviously not, thus \(\lim_{x\rightarrow c}f(x)\) does not exist
That was much easier than I expected.
now, since we cant just fill in one point and make it continuous, i.e. there is no one point that we can add so that we can draw the entire graph without lifting the pencil and thus is does not have a removable discontinuity .
I see now. Thank you! :)
np

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