Questions from General Calculus

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

Compute f (g (x)), where f (x) and g (x) are the following: f (x) = x (x2 + 1), g (x) = √x

Q: When a drug or vitamin is administered intramuscularly (into a muscle

When a drug or vitamin is administered intramuscularly (into a muscle), the concentration in the blood at time t after injection can be approximated by a function of the form The graph of f (t) = 5...

Q: Under certain geographic conditions, the wind velocity υ at a height

Under certain geographic conditions, the wind velocity υ at a height x centimeters above the ground is given by υ = K ln(x/x0), where K is a positive constant (depending on the air density, average wi...

Q: Let R(x) be the revenue received from the sale

Let R(x) be the revenue received from the sale of x units of a product. The average revenue per unit is defined by AR = R(x)/x. Show that at the level of production where the average revenue is maximi...

Q: Find k such that 2x = ekx for all x.

Find k such that 2x = ekx for all x.

Q: Find k such that 2-x/5 = ekx for

Find k such that 2-x/5 = ekx for all x.

Q: Graph the function y = ln(ex), and use trace

Graph the function y = ln(ex), and use trace to convince yourself that it is the same as the function y = x. What do you observe about the graph of y = eln x?

Q: Graph y = e2x and y = 5 together, and determine

Graph y = e2x and y = 5 together, and determine the x-coordinate of their point of intersection (to four decimal places). Express this number in terms of a logarithm.

Q: Graph y = ln 5x and y = 2 together and determine

Graph y = ln 5x and y = 2 together and determine the x-coordinate of their point of intersection (to four decimal places). Express this number in terms of a power of e.

Q: Consider the function f (x) = 5(1 -

Consider the function f (x) = 5(1 - e-2x), x ≥ 0. (a) Show that f (x) is increasing and concave down for all x ≥ 0. (b) Explain why f (x) approaches 5 as x gets large. (c) Sketch the graph of f (x), x...