Question 1

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.

Accepted Answer

A)   
B)   
C)   
D)

Question 2

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

Accepted Answer

A)  5 
B)  16 
C)  8 
D)  3

Question 3

Provide an appropriate response.
-Evaluate.

Accepted Answer

A)  5 
B)  -4 
C)   
D)

Question 4

Find the partial derivative.
-Find

Accepted Answer

A)  -32 
B)  20 
C)  92 
D)  -20

Question 5

Provide an appropriate response.
-Evaluate

Accepted Answer

A)  450 
B)  30 
C)  -450 
D)  -480

Question 6

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

Accepted Answer

A)   
B)   
C)   
D)

Question 7

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.

Accepted Answer

A)   
B)   
C)   
D)

Question 8

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

Accepted Answer

A)  26 
B)  38 
C)  28 
D)  36

Question 9

Find the partial derivative.
-Find

Accepted Answer

A)  - 86 
B)  170 
C)  86 
D)  -170

Question 10

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

Accepted Answer

A)  y = 0.74x + 23.04 
B)  y = - 0.74x - 23.04 
C)  y = 1.29x - 26.83 
D)  y = 13.46x + 0.04

Question 11

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

Accepted Answer

A)   
B)   
C)   
D)

Question 12

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

Accepted Answer

A)  6 
B)   
C)   
D)  8

Question 13

Provide an appropriate response.
-Find fxy for

Accepted Answer

A)   
B)   
C)   
D)

Question 14

Provide an appropriate response.
-Find the critical points for

Accepted Answer

A)  (-2, -1) 
B)  (-2, 1) 
C)  (2, -1) 
D)  (2, 1)

Question 15

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.

Accepted Answer

A)  $20,565 
B)  $50,195 
C)  $49,975 
D)  $29,415

Question 16

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

Accepted Answer

A)  8 
B)  2 
C)  1 
D)  4

Question 17

Provide an appropriate response.
-Find the local extrema for

Accepted Answer

A)  f(5, 2) = -13 is a minimum 
B)  f(1, 1) = -1 is a minimum 
C)  f(-5, 2) = 55 is a maximum 
D)  f(0, 0) = 1 is a minimum

Question 18

Choose the surface that the function describes.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 19

Provide an appropriate response.
-For

Accepted Answer

A)   
B)   
C)  12 
D)

Question 20

Provide an appropriate response.
-Evaluate  .

Accepted Answer

A)   
B)   
C)   
D)

Exam 7: Multivariable Calculus

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

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 .