Questions from General Calculus

Q: Find the area of the region between y = x2 - 3x

Find the area of the region between y = x2 - 3x and the x-axis (a) from x = 0 to x = 3, (b) from x = 0 to x = 4, (c) from x = -2 to x = 3.

Q: Find the area of the region between y = x2 and y

Find the area of the region between y = x2 and y = 1/x2 (a) from x = 1 to x = 4, (b) from x = 1/2 to x = 4.

Q: Determine the following: ∫3e-2x dx

Determine the following: ∫3e-2x dx

Q: Find the area in Fig. 27 of the region bounded by

Find the area in Fig. 27 of the region bounded by y = 1/x2, y = x, and y = 8x, for x ≥ 0. Figure 27:

Q: Find the area of the region bounded by y = 1/

Find the area of the region bounded by y = 1/x, y = 4x, and y = x/2, for x ≥ 0. (The region resembles the shaded region in Exercise 29.) Figure 27:

Q: A helicopter is rising straight up in the air. Its velocity

A helicopter is rising straight up in the air. Its velocity at time t is υ(t) = 2t + 1 feet per second. (a) How high does the helicopter rise during the first 5 seconds? (b) Represent the answer to pa...

Q: After t hours of operation, an assembly line is producing lawn

After t hours of operation, an assembly line is producing lawn mowers at the rate of r(t) = 21 – 4/5 t mowers per hour. (a) How many mowers are produced during the time from t = 2 to t = 5 hours? (b)...

Q: Suppose that the marginal cost function of a handbag manufacturer is C

Suppose that the marginal cost function of a handbag manufacturer is C(x) = 3/32 x2 - x + 200 dollars per unit at production level x (where x is measured in units of 100 handbags). (a) Find the total...

Q: Suppose that the marginal profit function for a company is P(

Suppose that the marginal profit function for a company is P(x) = 100 + 50x - 3x2 at production level x. (a) Find the extra profit earned from the sale of 3 additional units if 5 units are currently...

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

Let M(x) be a company’s marginal profit at production level x. Give an economic interpretation of the number 44∫48 M(x)dx.