Question 1

Calculate  when defined.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

The temperature at the point  on the square with vertices (0, 0), (0, 3), (3, 0)and (3, 3)is given by  Find the hottest and coldest points on the square.

Accepted Answer

A) (4, 4), (0, 0) 
B) (3, 3), (0, 0) 
C) (0, 3), (0, 0) 
D) (3, 0), (0, 0) 
E) (3, 3), (1, 0)

Question 3

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 57 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight?

Accepted Answer

A) 6,859 in.3 
B) 185,193 in.3 
C) 57 in.3 
D) 114 in.3 
E) 19 in.3

Question 4

Find the average value of the given function over the indicated domain.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

What point on the surface  is closest to the origin?  Hint : Minimize the square of the distance from ( x , y , z )to the origin.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Calculate  when defined.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Suppose your newspaper is trying to decide between two competing desktop publishing software packages, Macro Publish and Turbo Publish. You estimate that if you purchase x copies of Macro Publish and y copies of Turbo Publish, your company s daily productivity will be  where U ( x , y )is measured in pages per day ( U is called a utility function.)If x = y = 13, by approximately how many pages per day will productivity increase if x is increased by one unit?

Accepted Answer

A) A productivity increase of approximately 9.17 pages per day. 
B) A productivity increase of approximately 3.59 pages per day. 
C) A productivity increase of approximately 4.59 pages per day. 
D) A productivity decrease of approximately 65.00 pages per day. 
E) A productivity increase of approximately 69.59 pages per day.

Question 8

Sketch the graph of the function.

Accepted Answer

A)   
B)   
C)   
D)

Question 9

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model.  where x is the reduction in sulfur emissions, y is the reduction in lead emissions (in pounds of pollutant per day), and C is the daily cost to the firm (in dollars)of this reduction. Government clean-air subsidies amount to $200 per pound of sulfur and $50 per pound of lead removed. How many pounds of pollutant should the firm remove each day to minimize the net cost (cost minus subsidy)?

Accepted Answer

A) 1 lb of sulfur and 1 lb of lead 
B) 1 lb of sulfur and 2 lb of lead 
C) 1 lb of sulfur and 0.5 lb of lead 
D) 0.5 lb of sulfur and 1 lb of lead 
E) 1.9 lb of sulfur and 1 lb of lead

Question 10

Find the point on the given plane closest to (1,1,0).

Accepted Answer

A) (-3, 5, 4) 
B) (-4, 4, 2) 
C) (-1, 3, 8) 
D) (-3, 5, 8) 
E) (3, 5, 8)

Question 11

Calculate  when defined.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

For the function  find  . Express the answer as a decimal rounded to four decimal places.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Compute the integral.

Accepted Answer

A) 81 
B) 41 
C) -5 
D) 3 
E) 0

Exam 8: Functions of Several Variables

Calculate when defined.

The temperature at the point on the square with vertices (0, 0) , (0, 3) , (3, 0) and (3, 3) is given by Find the hottest and coldest points on the square.

Trans World Airlines (TWA) has a rule for checked baggage, "The total dimensions (length + width + height) may not exceed 57 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight?

Find the average value of the given function over the indicated domain.

What point on the surface is closest to the origin? Hint : Minimize the square of the distance from ( x , y , z ) to the origin.

Calculate when defined.

Sketch the graph of the function.

Find the point on the given plane closest to (1,1,0) .

Calculate when defined.

For the function find . Express the answer as a decimal rounded to four decimal places.

Compute the integral.