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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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03:47
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 2
The Limit of a Function
Limits
Derivatives
Harvey Mudd College
Baylor University
University of Nottingham
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
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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
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