Exam 7: Multivariable Calculus

Solve the problem. -An industrial plant located in the center of a small town emits particulate matter into the atmosphere. Suppose the concentration of particulate matter in parts per million at a point d miles from the plant is given by C = 120 - 15d2. If the boundaries of the town form a rectangle four miles long and six miles wide, what is the Average concentration of particulate matter throughout the city? Express C as a function of x and y, set up a Double integral, and evaluate.

Find the value. -Find f(-8, 8) when f(x, y) = 3x + 5y - 8

Provide an appropriate response. -Evaluate.

Find the partial derivative. -Find

Provide an appropriate response. -Evaluate

Choose the surface that the function describes. -f(x, y) = 1 - x - 2y

Solve the problem. -The surface area of a human body (in square meters) is approximated by A = 0.202W(.425)H(.725), where W is the weight of the person in kilograms and H is the height in meters. Find A if W = 74 and H = 1.61.

Provide an appropriate response. -Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.

Find the partial derivative. -Find

Provide an appropriate response. -Find the least squares line for the following data:

Solve the problem. -A company has the following production function for a certain product Find the marginal productivity with fixed capital, Px .

Provide an appropriate response. -Find the double integral over the rectangular region R with the given boundaries.

Provide an appropriate response. -Find fxy for

Provide an appropriate response. -Find the critical points for

Solve the problem. -The marketing research department of a large manufacturing company has determined that the demand equations for two major items it produces are given by p = 2,000 - 5x + 8y and q = 4,000 + 9x - 7y where p is the Price of item A, q is the price of item B, x is the monthly demand for item A, and y is the monthly demand for Item B. Find the total monthly revenue from items A and B when x = 15 and y = 5.

Provide an appropriate response. -Find the average value of over the rectangle

Provide an appropriate response. -Find the local extrema for

Choose the surface that the function describes. -

Provide an appropriate response. -For

Provide an appropriate response. -Evaluate .