Questions from General Calculus

Q: A manufacturer of microcomputers estimates that t months from now it will

A manufacturer of microcomputers estimates that t months from now it will sell x thousand units of its main line of microcomputers per month, where x = .05t2 + 2t + 5. Because of economies of scale, t...

Q: If f (x) and g (x) are differentiable

If f (x) and g (x) are differentiable functions, find g (x) if you know that d/dx f ( g (x)) = 3x2 * f (x3 + 1).

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

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

Q: Determine the following: ∫k2 dx (k a constant

Determine the following: ∫k2 dx (k a constant)

Q: A company’s marginal cost function is .1x2 - x + 12

A company’s marginal cost function is .1x2 - x + 12 dollars, where x denotes the number of units produced in 1 day. (a) Determine the increase in cost if the production level is raised from x = 1 to x...

Q: A company’s marginal cost function is given by C(x)

A company’s marginal cost function is given by C(x) = 32 + x/20, where x denotes the number of items produced in 1 day and C(x) is in thousands of dollars. Determine the increase in cost if the compa...

Q: An investment grew at an exponential rate R(t) =

An investment grew at an exponential rate R(t) = 700e0.07t + 1000, where t is in years and R(t) is in dollars per year. Approximate the net increase in value of the investment after the first 10 years...

Q: A property with an appraised value of $200,000 in

A property with an appraised value of $200,000 in 2015 is depreciating at the rate R(t) = -8e-0.04t, where t is in years since 2015 and R(t) is in thousands of dollars per year. Estimate the loss in v...

Q: The rate of change of a population with emigration is given by

The rate of change of a population with emigration is given by P(t) = 7/300 et/25 – 1/80 et/16, where P(t) is the population in millions, t years after the year 2000. (a) Estimate the change in popul...

Q: You took a $200,000 home mortgage at an annual

You took a $200,000 home mortgage at an annual interest rate of 3%. Suppose that the loan is amortized over a period of 30 years, and let P(t) denote the amount of money (in thousands of dollars) that...