Exam 15: Integration

Find dy if y = .

Use differentials to approximate the change in the volume V of a sphere if the radius r is increased from 5 cm to 5.3 cm.(Hint: Use V = π .)

A company has determined that its marginal cost function (in dollars)is given by where x is the number of units made.Find the total cost for making 6 units by finding the area in the first quadrant bounded by and the lines y = 0,x = 0,and x = 6.

=

Use differentials only to find an approximate value of .

The rate of change of the value of a house that cost $250,000 to build can be modeled by = 7.5 ,where t is the time in years since the house was built,and V is the value (in hundreds of thousands of dollars)of the house.Find V(t).

If y' = 6x - 3 and y(2)= 4,then y =

The acceleration of an object after t seconds is given by the velocity at 4 seconds is given by and the position at 0 seconds is given by Find y(t).

dx =

Given the marginal cost function = 2q + 50,where c is in dollars,how much would it cost to increase production from q = 50 to q = 100?

Evaluate:

Use your graphing calculator to find the area between the x-axis and and the x-axis on the interval 2 ≤ x ≤ 5.Verify your result by finding

Suppose that in the United States the rate of change of the percentage of workers who belong to unions can be modeled by = 0.24(0.1x + - 0.02(0.1x + 8)where x is the number of years after 1940.Find y.

Determine:

=

Use differentials to approximate .

If y = ,use differentials to approximate the change in y if x changes from 25 to 25.3.

=

If the marginal cost for a company is f(x)= 6,find

Determine: dx