Question 1

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

Accepted Answer

A)  18 
B)  36 
C)  10 
D)  27 
A)  18 
B)  36 
C)  10 
D)  27

Question 2

Solve the problem.
-Suppose that the labor cost for a building is approximated by   where x is the number of days of skilled labor and y is the number of days of semiskilled labor required. Find the x and
Y that minimize cost C.

Accepted Answer

A)  x = 8, y = 210 
B)  x = 105, y = 42 
C)  x = 4, y = 105 
D)  x = 42, y = 315 
A)  x = 8, y = 210 
B)  x = 105, y = 42 
C)  x = 4, y = 105 
D)  x = 42, y = 315

Question 3

Provide an appropriate response.
-Find the volume of the solid under the graph of   over the rectangle

Accepted Answer

A)    
B)    
C)  -12 
D)    
A)    
B)    
C)  -12 
D)

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Find the partial derivative.
-Find

Accepted Answer

A)  8 
B)  -48 
C)  16 
D)  40 
A)  8 
B)  -48 
C)  16 
D)  40

Question 6

Provide an appropriate response.
-Refer to the table given below. Find the least squares line and use it to estimate y when x = 15.

Accepted Answer

The answer of Provide an appropriate response.
-Refer to the table...

Question 7

Provide an appropriate response.
-Consider the following data on the growth of peach grafts under controlled conditions.   Find the regression line y = ax + b.

Accepted Answer

A)  y = 13x + 8.19 
B)  y = 1.33x + 0.21 
C)  y =1.50 x + 0.7 
D)  y = -2.10x + 0.2 
A)  y = 13x + 8.19 
B)  y = 1.33x + 0.21 
C)  y =1.50 x + 0.7 
D)  y = -2.10x + 0.2

Question 8

Solve the problem.
-The profit function for sales of two models of television sets at a chain discount store is given by   where x is the number of sales per week of model A, and y is the number of sales per week of model B. Find Px(10, 15) and interpret the result.

Accepted Answer

A)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $60 
B)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $80. 
C)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $120 
D)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $140 
A)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $60 
B)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $80. 
C)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $120 
D)    At a sales level of 10 units of model A and 15 units of model B, increasing sales of model A by one unit and holding
Sales of model B at 15 units will increase profit by approximately $140

Question 9

Provide an appropriate response.
-Use Lagrange multipliers to minimize   subject to x - y = 10.

Accepted Answer

A)  f(5, -5) = 75 
B)  f(5, 5) = 25 
C)  f(1, 2) = 3 
D)  f(2, -1) = 7 
A)  f(5, -5) = 75 
B)  f(5, 5) = 25 
C)  f(1, 2) = 3 
D)  f(2, -1) = 7

Question 10

Solve the problem.
-The total cost to produce MP3 players in 2 models is given by   where red model is x and the green one is y. If a total of 60 players must be made, how should production be allocated so that the total cost is minimized?

Accepted Answer

A)  60 red players and 0 green players 
B)  30 red players and 30 green players 
C)  0 red players and 60 green players 
D)  59 red players and 1 green players 
A)  60 red players and 0 green players 
B)  30 red players and 30 green players 
C)  0 red players and 60 green players 
D)  59 red players and 1 green players

Question 11

Solve the problem.
-Under ideal conditions, if a person driving a car slams on the brakes and skids to a stop on wet pavement, the length of the skid marks (in feet) is given by the formula L(x, y) = 0.00002xy2, where x is the weight of the car in
Pounds and y is the speed of the car in miles per hour. What is the average length of the skid marks for cars
Weighing between 2500 and 3500 pounds and traveling at speeds between 45 and 55 miles per hour? Set up a
Double integral and evaluate.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Solve the problem.
-The Cobb-Douglas function for a new product is given by   where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of
Labor costs $40, and each unit of capital costs $80. If $400,000 has been budgeted for the production of this
Product, determine how this amount should be allocated in order to maximize production, and find the
Maximum production.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Solve the problem.
-The production function z for an industrial country was estimated as   where x is the amount of labor and y, the amount of capital. Find the marginal productivity of labor.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Evaluate.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Solve the problem.
-The rectangular box below, with an open top and one partition, is to be constructed from 18 square inches of cardboard. Find the dimensions that will result in a box with the largest possible volume.

Accepted Answer

A)  2 inches by 3 inches by 1 inch 
B)  2 inches by 2 inches by 1 inch 
C)  3 inches by 2 inches by 1 inch 
D)  3 inches by 3 inches by 1 inch 
A)  2 inches by 3 inches by 1 inch 
B)  2 inches by 2 inches by 1 inch 
C)  3 inches by 2 inches by 1 inch 
D)  3 inches by 3 inches by 1 inch

Question 16

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

Accepted Answer

A)  y = 0.18x + 5.90 
B)  y = 0.18x - 5.90 
C)  y = - 0.18x + 5.90 
D)  y = - 0.18x - 5.90 
A)  y = 0.18x + 5.90 
B)  y = 0.18x - 5.90 
C)  y = - 0.18x + 5.90 
D)  y = - 0.18x - 5.90

Question 17

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

Accepted Answer

A)  y = -0.3x + 1.2 
B)  y = 0.3x - 1.2 
C)  y = -0.13x - 1.2 
D)  y = 0.13x - 1.2 
A)  y = -0.3x + 1.2 
B)  y = 0.3x - 1.2 
C)  y = -0.13x - 1.2 
D)  y = 0.13x - 1.2

Question 18

Provide an appropriate response.
-Give a verbal description of the region   and determine whether R is a regular x region, regular y region, both, or neither.

Accepted Answer

A)  R consists of the points on or inside the rectangle with corners (±3, ±6); both 
B)  R consists of the points on or inside the rectangle with corners (±6, ±3); regular x region 
C)  R consists of the points on or inside the rectangle with corners (±6, ±3); both 
D)  R consists of the points on or inside the rectangle with corners (±6, ±3); neither 
A)  R consists of the points on or inside the rectangle with corners (±3, ±6); both 
B)  R consists of the points on or inside the rectangle with corners (±6, ±3); regular x region 
C)  R consists of the points on or inside the rectangle with corners (±6, ±3); both 
D)  R consists of the points on or inside the rectangle with corners (±6, ±3); neither

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

Solve the problem. -Suppose that the labor cost for a building is approximated by where x is the number of days of skilled labor and y is the number of days of semiskilled labor required. Find the x and Y that minimize cost C.

Provide an appropriate response. -Find the volume of the solid under the graph of over the rectangle

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

Find the partial derivative. -Find

Provide an appropriate response. -Refer to the table given below. Find the least squares line and use it to estimate y when x = 15.

Provide an appropriate response. -Consider the following data on the growth of peach grafts under controlled conditions. Find the regression line y = ax + b.

Solve the problem. -The profit function for sales of two models of television sets at a chain discount store is given by where x is the number of sales per week of model A, and y is the number of sales per week of model B. Find Px(10, 15) and interpret the result.

Provide an appropriate response. -Use Lagrange multipliers to minimize subject to x - y = 10.

Solve the problem. -The total cost to produce MP3 players in 2 models is given by where red model is x and the green one is y. If a total of 60 players must be made, how should production be allocated so that the total cost is minimized?

Solve the problem. -The production function z for an industrial country was estimated as where x is the amount of labor and y, the amount of capital. Find the marginal productivity of labor.

Evaluate. -

Solve the problem. -The rectangular box below, with an open top and one partition, is to be constructed from 18 square inches of cardboard. Find the dimensions that will result in a box with the largest possible volume.

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

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

Provide an appropriate response. -Give a verbal description of the region and determine whether R is a regular x region, regular y region, both, or neither.

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters

Exam 7: Multivariable Calculus

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

Solve the problem. -Suppose that the labor cost for a building is approximated by where x is the number of days of skilled labor and y is the number of days of semiskilled labor required. Find the x and Y that minimize cost C.

Provide an appropriate response. -Find the volume of the solid under the graph of over the rectangle

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

Find the partial derivative. -Find

Provide an appropriate response. -Refer to the table given below. Find the least squares line and use it to estimate y when x = 15.

Provide an appropriate response. -Consider the following data on the growth of peach grafts under controlled conditions. Find the regression line y = ax + b.

Solve the problem. -The profit function for sales of two models of television sets at a chain discount store is given by where x is the number of sales per week of model A, and y is the number of sales per week of model B. Find Px(10, 15) and interpret the result.

Provide an appropriate response. -Use Lagrange multipliers to minimize subject to x - y = 10.

Solve the problem. -The total cost to produce MP3 players in 2 models is given by where red model is x and the green one is y. If a total of 60 players must be made, how should production be allocated so that the total cost is minimized?

Solve the problem. -The production function z for an industrial country was estimated as where x is the amount of labor and y, the amount of capital. Find the marginal productivity of labor.

Evaluate. -

Solve the problem. -The rectangular box below, with an open top and one partition, is to be constructed from 18 square inches of cardboard. Find the dimensions that will result in a box with the largest possible volume.

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

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

Provide an appropriate response. -Give a verbal description of the region and determine whether R is a regular x region, regular y region, both, or neither.

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters