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Explain what it means to say that

$ \displaystyle \lim_{x\to1^-}f(x) = 3 $ and $ \displaystyle \lim_{x\to1^+}f(x) = 7 $

In this situation is it possible that $ \displaystyle \lim_{x\to1}f(x) $ exists?

Explain.

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So here we have a graph. And let's say that the limit As extra approaches one from the left as a five X is equal to three, that would look something like this. Our function as it approaches Our X Coordinate one. Our white corner is approaching three. All right now, let's say we also had a limit As X approaches one from the right. And that is what our plus sign here means here are negative means from the left. Plus is from the right Is F of X is equal to seven. Balance. Say I would look like something let's say like this. So here our function as we approach from the right side as we are approaching one on the X coordinate, Our function is approaching seven on the Y coordinate from the left. It's as we're approaching one on the X cornets approaching three. So as our limit is approaching one from the left, it's not equal to our limit As X approaches one from the right, meaning that there is no limit at X equals one.

Georgia Southern University