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A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount $ f(t) $ of the drug in the bloodstream after $ t $ hours. Find

$ \displaystyle \lim_{t\to 12^-}f(t) $ and $ \displaystyle \lim_{t\to 12^+}f(t) $

and explain the significance of these one-sided limits.

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Missouri State University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

So in this problem we are given a graph of an injection look something like this, where this is for a Well 16, these are T and ours. And this is the 150 mg injection and up here Is 300 mg ejection. Okay? Were asked to determine the limit as T approaches 12 minus F t. Well, this is the left limit, which is the significance here. This is approaching 12. were going towards 12 from we left. So as we go through 12 from this side and we go down this curve, Which turns out to be right at that 150. So this is 150 mg. They were asked to determine T approaching 12 from the right of Fft. This is the right limit Means we go to 12 from the right just coming this way, which is going up this curve. So that means we are at 300 milligrams. And so we have the two limits, the left and the right limit. And the significance here is that they are not equal as this is not a continuous function