Questions from General Calculus

Q: Find the area of the region between the curves y = 2x2

Find the area of the region between the curves y = 2x2 + x and y = x2 + 2 from x = 0 to x = 2.

Q: Find the function f (x) for which f ‘

Find the function f (x) for which f ‘(x) = (x - 5)2, f (8) = 2.

Q: Find the function f (x) for which f ‘(

Find the function f (x) for which f ‘(x) = e-5x, f (0) = 1.

Q: Describe all solutions of the following differential equations, where y represents

Describe all solutions of the following differential equations, where y represents a function of t. (a) y’ = 4t (b) y’ = 4y (c) y’ = e4t

Q: Let k be a constant, and let y = f (

Let k be a constant, and let y = f (t) be a function such that y’ = kty. Show that y = Cekt2/2, for some constant C.

Q: An airplane tire plant finds that its marginal cost of producing tires

An airplane tire plant finds that its marginal cost of producing tires is .04x + $150 at a production level of x tires per day. If fixed costs are $500 per day, find the cost of producing x tires per...

Q: Find the value of k that makes the antidifferentiation formula true.

Find the value of k that makes the antidifferentiation formula true. ∫ (4 - x)-1 dx = k ln |4 – x| + C

Q: If the marginal revenue function for a company is 400 - 3x2

If the marginal revenue function for a company is 400 - 3x2, find the additional revenue received from doubling production if 10 units are currently being produced.

Q: A drug is injected into a patient at the rate of f

A drug is injected into a patient at the rate of f (t) cubic centimeters per minute at time t. What does the area under the graph of y = f (t) from t = 0 to t = 4 represent?

Q: A rock thrown straight up into the air has a velocity of

A rock thrown straight up into the air has a velocity of υ(t) = -9.8t + 20 meters per second after t seconds. (a) Determine the distance the rock travels during the first 2 seconds. (b) Represent the...