Exam 15: Integration

Use differentials to approximate: .

A company has determined that its marginal revenue function (in dollars)is given by where x is the number of units sold.Find the total revenue for selling 4 units by finding the area in the first quadrant bounded by and the lines y = 0,x = 0,and x = 4.

Determine:

Determine: dx

The height of a cylinder is decreasing at a rate of = -12 .Find h as a function of t.

A factory is dumping garbage into a river at a rate given by = tons per month,where t is the time in months since the dumping began and x is the number of tons of garbage.Find the function x(t)which gives the total number of tons of garbage dumped.

Determine: dx

Determine:

A factory is dumping garbage into a river at a rate given by = tons per month,where t is the time in months since the dumping began and x is the number of tons of garbage.Find the function x(t)which gives the total number of tons of garbage dumped.

Determine: dx

If q = - 6 + 3p - 8,find when p = 1.

Determine:

Use differentials to approximate: ln(0.95).

Determine: dx

=

Suppose the rate of savings in a country is given by = 2.7 - 400t + 9000,where t is the time in years,and S is the amount of money saved in billions of dollars.Find the function S(t)which gives the total amount of money saved.You may assume that $0 is saved at t = 0.

Determine:

After weeks of television promotion,an electronics store finds that its sales change at a rate given by where t is the number of days after the advertising ends and S is in thousands of dollars.Find the total sales for the first week after the advertising ends.

An oil company estimates that for the next few months,oil will be pumped (in thousands of gallons per month)from a producing field at the rate of R(t)= + 5,where t is in months.Find

Determine: