Questions from General Calculus

Q: Let M(x) be a company’s marginal cost at production

Let M(x) be a company’s marginal cost at production level x. Give an economic interpretation of the number 0∫100 M(x)dx.

Q: Some food is placed in a freezer. After t hours,

Some food is placed in a freezer. After t hours, the temperature of the food is dropping at the rate of r(t) degrees Fahrenheit per hour, where r(t) = 12 + 4/(t + 3)2. (a) Compute the area under the g...

Q: Suppose that the velocity of a car at time t is υ

Suppose that the velocity of a car at time t is υ(t) = 40 + 8/(t + 1)2 kilometers per hour. (a) Compute the area under the velocity curve from t = 1 to t = 9. (b) What does the area in part (a) repres...

Q: Find all antiderivatives of each following function: f (x

Find all antiderivatives of each following function: f (x) = 9x8

Q: Determine the following: ∫ (7/2x3 – 3

Determine the following: ∫ (7/2x3 – 3√x) dx

Q: Deforestation is one of the major problems facing sub-Saharan Africa

Deforestation is one of the major problems facing sub-Saharan Africa. Although the clearing of land for farming has been the major cause, the steadily increasing demand for fuel wood has also become a...

Q: Refer to Exercise 39. The rate of new tree growth (

Refer to Exercise 39. The rate of new tree growth (in millions of cubic meters per year) in the Sudan t years after 1980 is given approximately by the function g(t) = 50 - 6.03e0.09t. Set up the defin...

Q: After an advertising campaign, a company’s marginal profit was adjusted up

After an advertising campaign, a company’s marginal profit was adjusted up from M1(x) = 2x2 - 3x + 11, before advertising, to M2(x) = 2x2 - 2.4x + 8, after advertising. Here x denotes the number of un...

Q: The marginal profit for a certain company is MP1(x)

The marginal profit for a certain company is MP1(x) = -x2 + 14x - 24. The company expects the daily production level to rise from x = 6 to x = 8 units. The management is considering a plan that would...

Q: Two rockets are fired simultaneously straight up into the air. Their

Two rockets are fired simultaneously straight up into the air. Their velocities (in meters per second) are υ1(t) and υ2(t), and υ1(t) ≥ υ2(t) for t ≥ 0. Let A denote the area of the region between the...