Exam 15: Integration

If the marginal revenue function for a manufacturer's product is = 1000 - 10q - 6 ,find the demand function.

Determine: dx

Determine:

dx =

The base of a triangle is decreasing at a rate of = - .Find b as a function of t.

Determine:

Determine:

=

Use differentials to approximate ln(0.99).

The producers of a new radio show expect the number of listeners (in hundreds)to increase at a rate of where x is the number of weeks after the show premiers.Find the total increase in listeners in the first four weeks by evaluating .

Determine:

A manufacturer of a product has a marginal cost function given by where c is the total cost (in dollars)of producing q units of a product.If fixed costs are $30,000,then the total cost of producing 30 units is

Determine: dx

The marginal price for a weekly demand of x bottles of shampoo is given by p'(x)= .Find p(x).

Find y subject to the given conditions: y'' = 6x - 2; y'(1)= 2; y(1)= 2.

For the region bounded by f(x)= 3x - 1,y = 0,x = 1,and x = 3,approximate the area by evaluating .(Use the left-hand endpoint of each subinterval.)

Determine:

If = 3 - 3 and y(0)= 8,then y(1)=

Use differentials and C = 250 + 0.30x to approximate the change in the cost C (in dollars)to produce x pounds of candy if the number of pounds of candy increases from 10 pounds to 10.6 pounds.

For a group of rats that were fed a particular diet,the rate of change of the average weight gain G (in grams)of a rat with respect to the percent P of yeast in the diet is If G = 36 when P = 8,find G.