Deck 8: Functions of Several Variables

Question 1

Graph the function.

A)
B)
C)
D)

Answer 1

Question 2

Graph the function.

A)
B)
C)
D)

Answer 2

Question 3

Sketch the graph of the function.

A)
B)
C)
D)

Answer 3

Question 4

Sketch the graph of the function.

A)
B)
C)
D)

Question 5

or the function show cross section at .

A)
B)
C)
D)

Question 6

Evaluate for

A)
B)
C)
D)
E)

Question 7

Evaluate for

A)
B)
C)
D)
E)

Question 8

Use the given tabular representation of the function to compute .

A)
B)
C)
D)
E)

Question 9

Graph the plane. =

A)
B)
C)
D)

Question 10

Sketch the graph of the function.

A)
B)
C)
D)

Question 11

Sketch the graph of the function.

A)
B)
C)
D)

Question 12

For the function find . Round to the nearest whole number if necessary.

A)11
B)10
C)12
D)13
E)17

Question 13

For the function find .

A)384
B)422
C)794
D)397
E)410

Question 14

Evaluate for

A)
B)
C)
D)
E)

Question 15

Graph the function.

A)
B)
C)
D)

Question 16

Sketch the graph of the function.

A)
B)
C)
D)

Question 17

Graph the function.

A)
B)
C)
D)

Question 18

Graph the function.

A)
B)
C)
D)

Question 19

Let . By what value is increased if is increased by 1?

A)5.4
B)4.4
C)1
D)42.9
E)38.5

Question 20

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

A)
B)
C)
D)
E)

Question 21

Use the given tabular representation of the function f to compute f (5, 10)- f (10, 5)..

Question 22

Graph the function.

A)
B)
C)
D)

Question 23

Your on-line bookstore is in direct competition with Amazon.com, BN.com, and Borders.com. Your company s daily revenue in dollars is given by where x , y , and z are the online daily revenues of Amazon.com, BN.com, and Borders.com, respectively. If Amazon.com and BN.com each show a daily revenue of $9,000, give an equation showing how your daily revenue depends on that of Borders.com.

A)R ( z )= 30,000 - 180 x - 90 y - 0.01 z + 0.0001 yz
B)R ( z )= 30,000 - 0.01 z
C)R ( z )= 29,730 + 0.89 z
D)R ( z )= 30,000 - 0.01 z + 0.0001 z
E)R ( z )= 29,730

Question 24

For the function show the cross section at .

A)
B)
C)
D)

Question 25

Your on-line bookstore is in direct competition with Amazon.com, BN.com, and Borders.com. Your company s daily revenue in dollars is given by where x , y , and z are the online daily revenues of Amazon.com, BN.com, and Borders.com, respectively. If Amazon.com and BN.com each show a daily revenue of $2,000, give an equation showing how your daily revenue depends on that of Borders.com.

Question 26

Cobb-Douglas productivity functions have the form where P stands for the number of items produced per year, x is the number of employees, and y is the annual operating budget. The numbers K and a are constants that depend on the situation we are looking at, with How many items will be produced per year by a company that has 150 employees and an annual operating budget of $70,000 if K = 1000 and a = 0.6? (Round your answer to one significant digit.)

A)1,000,000
B)2,000,000
C)3,000,000
D)1,752,645.1
E)2,752,645.1

Question 27

Your weekly cost (in dollars)to manufacture x cars and y trucks is What is the marginal cost of a truck? Please enter your answer as a number without the units.

Question 29

For the function show the cross section at .

A)
B)
C)
D)

Question 30

Evaluate for

Question 31

Graph the function.

A)
B)
C)
D)

Question 32

Cobb-Douglas productivity functions have the form where P stands for the number of items produced per year, x is the number of employees, and y is the annual operating budget. The numbers K and a are constants that depend on the situation we are looking at, with How many items will be produced per year by a company that has 200 employees and an annual operating budget of $100,000 if K = 1,000 and a = 0.6? (Round your answer to one significant digit.)

Question 33

The burden of human made aerosol sulfate in the earth s atmosphere, in grams per square meter, is where x is the total weight of aerosol sulfate emitted into the atmosphere per year and n is the number of years it remains in the atmosphere. A is the surface area of the earth, approximately square meters. Calculate the burden given the 1995 estimated values of grams per year and days. Enter the number of grams per square meter as a number without the units. Round to three decimal places.

A)0.168 grams per square meter
B)0.081 grams per square meter
C)0.040 grams per square meter
D)14.706 grams per square meter
E)1.048 grams per square meter

Question 34

Evaluate for

Question 35

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?

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 36

Evaluate for

Question 37

Your weekly cost (in dollars)to manufacture x cars and y trucks is What is the marginal cost of a car?

A)$244,000
B)$4,000
C)$246,000
D)$3,000
E)$6,000

Question 38

Let . By what value is increased if is increased by 1?

Question 39

Graph the function.

A)
B)
C)
D)

Question 40

For the function show the cross section at .

A)
B)
C)
D)

Question 41

Calculate when defined.

A)
B)
C)
D)
E)

Question 42

Calculate when defined.

A)
B)
C)
D)
E)

Question 44

Your weekly cost (in dollars)to manufacture cars and trucks is given by What is the marginal cost of a car? Of a truck?

A)Marginal cost of a car is 6,700 - 2.7183 e ^{0.05 ( x + y )} marginal cost of a truck is 3,400 - 2.7183 e ^{0.05 ( x + y )}
B)Marginal cost of a car is 6,700 - 2.7183 e ^{- 0.05 ( x - y )} marginal cost of a truck is 3,400 - 2.7 e ^{- 0.05 ( x - y )}
C)Marginal cost of a car is 3,400 + 2.7183 e ^{0.05 ( x + y )} marginal cost of a truck is 6,700 + 2.7183 e ^{0.05 ( x + y )}
D)Marginal cost of a car is 6,700 + 2.7183 e ^{- 0.05 ( x + y )} marginal cost of a truck is 3,400 + 2.7183 e ^{- 0.05 ( x + y )}
E)Marginal cost of a car is 6,700 + 2.7183 e ^{- 0.05 x} marginal cost of a truck is 3,400 + 2.7183 e ^{- 0.05 y}

Question 45

Calculate the values of at

A)
B)
C)
D)
E)

Question 46

Calculate when defined.

A)
B)
C)
D)
E)

Question 47

Calculate and evaluate each at .

A)
B)
C)
D)
E)

Question 48

Calculate when defined.

A)
B)
C)
D)
E)

Question 49

Calculate when defined.

A)
B)
C)
D)
E)

Question 50

Your weekly cost (in dollars)to manufacture cars and trucks is given by Compute the marginal cost of manufacturing cars at a production level of 15 cars and 14 trucks.

A)$3,425,200
B)$560
C)$6,100
D)$6,700
E)$6,140

Question 51

Calculate when defined.

A)
B)
C)
D)
E)

Question 52

Calculate when defined.

A)
B)
C)
D)
E)

Question 53

If positive electric charges of and coulombs are situated at positions and , respectively, then the force of repulsion they experience is given by where , is given in newtons, and all positions are measured in meters. Assume that a charge of 7 coulombs is situated at the origin and that a second charge of 15 coulombs is situated and moving in the direction at 1.9 meters per second. How fast is the electrostatic force it experiences decreasing? Round your answer to the nearest trillion.

A)
B)
C)
D)
E)

Question 54

Calculate when defined.

A)
B)
C)
D)
E)

Question 55

Calculate when defined.

A)
B)
C)
D)
E)

Question 56

Calculate when defined.

A)
B)
C)
D)
E)

Question 58

Your weekly cost (in dollars)to manufacture cars and trucks is given by Compute the marginal cost of manufacturing cars at a production level of 15 cars and 16 trucks. $ __________

Question 59

Calculate the values of at .

A)
B)
C)
D)
E)

Question 60

Your weekly cost (in dollars)to manufacture cars and trucks is given by Find

A)
B)
C)
D)
E)

Question 61

Your weekly cost (in dollars)to manufacture cars and trucks is given by Find NOTE: Please enter your answers without the units, separated by commas.

Question 62

Calculate and evaluate each at . Enter your answers, separated by a comma.

Question 65

In the table below, classify each highlighted value.

A)a relative minimum
B)a relative maximum
C)a saddle point
D)none of these

Question 66

Calculate when defined. Enter your answers, separated by a comma.

Question 67

Classify the highlighted value in the table.

A)a saddle point
B)a relative maximum
C)a relative minimum
D)none of these

Question 68

Locate the local maximum of the function.

A)(0, 0, 0)
B)(- 4, 4, -32)
C)( 4, 2, -32)
D)(- 4, - 2, 0)
E)(4, 4, -32)

Question 70

Locate the saddle point of the function.

A)(3, 1, -10)
B)(6, 1, - 1)
C)(6, 1, -10)
D)(3, 0, -10)
E)(6, 0, -10)

Question 71

Locate the critical point of the function.

A)(0,7,7)
B)(4, 3, 98)
C)(0, 0, 0)
D)(4, 3, 7)
E)(0, 0, 7)

Question 73

How many critical points does the following function have?

A)one
B)three
C)four
D)two
E)none

Question 74

Calculate when defined. Enter your answers, separated by a comma.

Question 75

Find when defined. Enter your answers, separated by a comma.

Question 76

Calculate when defined. Enter your answers, separated by a comma.

Question 77

Locate the local maximum of the function.

A)
B)
C)
D)
E)

Question 79

If positive electric charges of and coulombs are situated at positions and , respectively, then the force of repulsion they experience is given by where , is given in newtons, and all positions are measured in meters. Assume that a charge of 8 coulombs is situated at the origin and that a second charge of 15 coulombs is situated and moving in the direction at 1.4 meters per second. How fast is the electrostatic force it experiences decreasing? NOTE: Please enter your answer without the units. Round the answer to the nearest trillion.

Question 80

Locate the critical point of the function.

A)(4, 3,-27)
B)(-4, 3, 27)
C)(8, 6, 2)
D)(- 8, 6, 2)
E)(3, -4, 27)