Questions from General Calculus

Q: Physiologists usually describe the continuous intravenous infusion of glucose in terms of

Physiologists usually describe the continuous intravenous infusion of glucose in terms of the excess concentration of glucose, C(t) = A(t)/V, where V is the total volume of blood in the patient. In th...

Q: Differentiate the functions. y = x / (x +

Differentiate the functions. y = x / (x + 1/x)

Q: Compute f (g (x)), where f (x)

Compute f (g (x)), where f (x) and g (x) are the following: f (x) = (x + 1)/(x – 3), g (x) = x + 3

Q: A news item is broadcast by mass media to a potential audience

A news item is broadcast by mass media to a potential audience of 50,000 people. After t days, f (t) = 50,000(1 - e-0.3t) people will have heard the news. The graph of this function is shown in Fig....

Q: Describe an experiment that a doctor could perform to determine the velocity

Describe an experiment that a doctor could perform to determine the velocity constant of elimination of glucose for a particular patient.

Q: After a drug is taken orally, the amount of the drug

After a drug is taken orally, the amount of the drug in the bloodstream after t hours is f (t) = 122(e-0.2t - e-t) units. (a) Graph f (t), f (t), and f ‘(t) in the window [0, 12] by [-20, 75] (b) How...

Q: Differentiate the functions. y = x(x2 + 1

Differentiate the functions. y = x(x2 + 1)4

Q: Let s(t) be the number of miles a car

Let s(t) be the number of miles a car travels in t hours. Then, the average velocity during the first t hours is / miles per hour. If the average velocity is maximized at time t0, show that at this ti...

Q: A model incorporating growth restrictions for the number of bacteria in a

A model incorporating growth restrictions for the number of bacteria in a culture after t days is given by f (t) = 5000(20 + te-0.04t). (a) Graph f (t) and f ‘(t) in the window [0, 100] by [-700, 300...

Q: Consider the function g(x) = 10 - 10e-

Consider the function g(x) = 10 - 10e-0.1x, x ≥ 0. (a) Show that g(x) is increasing and concave down for x ≥ 0. (b) Explain why g(x) approaches 10 as x gets large. (c) Sketch the graph of g(x), x ≥ 0....