Questions from General Calculus

Q: Let f (x) = 2x – tan x, -

Let f (x) = 2x – tan x, -π/2 < x < π/2. On what interval is f concave downward?

Q: (a). Sodium chlorate crystals are easy to grow in the

(a). Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calc...

Q: If xy + ey = e, find the value of y

If xy + ey = e, find the value of y" at the point where x = 0.

Q: A particle moves according to a law of motion s = f

A particle moves according to a law of motion s = f (t), t > 0, where is measured in seconds and in feet. (a). Find the velocity at time t. (b). What is the velocity after 3 s? (c). When is the partic...

Q: A particle moves according to a law of motion s = f

A particle moves according to a law of motion s = f (t), t > 0, where is measured in seconds and in feet. (a). Find the velocity at time t. (b). What is the velocity after 3 s? (c). When is the partic...

Q: (a). The volume of a growing spherical cell is V

(a). The volume of a growing spherical cell is V = 4/3πr3, where the radius is measured in micrometers (1 µm = 10-6 m). Find the average rate of change of with respect to when changes from (i). 5 to 8...

Q: Match the graph of each function in (a)–(d)

Match the graph of each function in (a)–(d) with the graph of its derivative in I–IV. Give reasons for your choices.

Q: Trace or copy the graph of the given function f. (

Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it.

Q: Refer to the law of laminar flow given in Example 7.

Refer to the law of laminar flow given in Example 7. Consider a blood vessel with radius 0.01 cm, length 3 cm, pressure difference 3000 dynes/cm2, and viscosity η = 0.027. (a). Find the velocity of th...

Q: In a fish farm, a population of fish is introduced into

In a fish farm, a population of fish is introduced into a pond and harvested regularly. A model for the rate of change of the fish population is given by the equation where r0 is the birth rate of the...