Exam 15: Integration

Determine: dx

Determine: ds

Find the differential in terms of x and dx. y =

A manufacturer's marginal cost function is = .1q + 7.Determine the cost involved to increase production from 40 to 60 units.

Evaluate:

Use differentials to approximate the change in the wattage W of a flood light with a resistance R = 8 ohms,if the current I is increased from 4 amperes to 4.2 amperes.(Hint: Use W = .)

The income (in dollars)from a fast food chain is increasing at a rate of f(t)= 10,000 where t is in years.Find the total income for the chain over the first three years.

Determine: dt

Suppose that in the United States the rate of change of the percentage of workers who belong to unions can be modeled by = 0.15(0.2x + - 1.4(0.2x+ 3),where x is the number of years after 1940.Find y.

For the region bounded by f(x)= 4 - x,y = 0,x = 0,and x = 3,approximate the area by evaluating .(Use the right-hand endpoint of each subinterval.)

A company has determined that its marginal revenue function (in dollars)is given by where x is the number of units made.Find the total revenue for making 6 units by evaluating .

The marginal revenue for a product is given by = + 998.Find r.

The producers of a long running radio show expect the number of listeners (in hundreds)to decrease at a rate of L'(x)= -5 - ,where x is the number of weeks after the first day of the year.Find the total decrease in listeners in the first 2 weeks by evaluating .

Determine:

The marginal cost function for a manufacturer's product is given by where c is in dollars.Find the cost function if fixed costs are $100.

Determine:

Use differentials and R = 300x+ 50 - to approximate the change in revenue R (in dollars)from selling x pounds if the number of pounds increases from 10 to 10.2.

The supply equation for a company is q = .Find from .

The supply equation for a company is q = 4 + 3.Find from .

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