Single Variable Calculus

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Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 10

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The given graph shows the amount $f(t)$ of the drug in the blood stream of a patient after $t$ hours. Suppose a patient receives a $150 \, mg$ injection of a drug every 4 hours. Find $\lim\limits_{x \rightarrow 12^-} f(x)$ and $\lim\limits_{x \rightarrow 12^+} f(t)$ and explain the significance of these one-sided limits.

Referring to the graph given the values of $\lim \limits_{t \to 12^-} f(t) = 150$ and $\lim \limits_{t \to 12^+} f(t) = 300$

The significance of these limits pertains to the change in the amount of drugs before and after the fourth injection. The amount of drugs right before the injection is represented by the left hand limit while the other is represented by the right hand limit.

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