Question 1

Let   Compute the following. g(1, 1, 1), g(- 1, 0, 1), g(- 1, 1, 1)

Accepted Answer

A) g(1, 1, 1) = - e, g(- 1, 0, 1) = - 1, g(- 1, 1, 1) = - 1 
B) g(1, 1, 1) = 1, g(- 1, 0, 1) = - e, g(- 1, 1, 1) = - 1 
C) g(1, 1, 1) = - 1, g(- 1, 0, 1) = 1, g(- 1, 1, 1) = - e 
D) g(1, 1, 1) = e, g(- 1, 0, 1) = - 1, g(- 1, 1, 1) = - e 
A) g(1, 1, 1) = - e, g(- 1, 0, 1) = - 1, g(- 1, 1, 1) = - 1 
B) g(1, 1, 1) = 1, g(- 1, 0, 1) = - e, g(- 1, 1, 1) = - 1 
C) g(1, 1, 1) = - 1, g(- 1, 0, 1) = 1, g(- 1, 1, 1) = - e 
D) g(1, 1, 1) = e, g(- 1, 0, 1) = - 1, g(- 1, 1, 1) = - e D

Question 2

Let   Compute the following. f(1, 2), f(2, - 1)

Accepted Answer

A) f(1, 2) = 12, f(2, - 1) = 3 
B) f(1, 2) = 13, f(2, - 1) = 6 
C) f(1, 2) = 3, f(2, - 1) = 13 
D) f(1, 2) = 11, f(2, - 1) = 5 
A) f(1, 2) = 12, f(2, - 1) = 3 
B) f(1, 2) = 13, f(2, - 1) = 6 
C) f(1, 2) = 3, f(2, - 1) = 13 
D) f(1, 2) = 11, f(2, - 1) = 5 D

Question 3

Maximize the function   subject to the constraint   .

Accepted Answer

The answer of Maximize the function   subject to...

Question 4

If   is a function of x and y, then there are functions   and   of one variable such a that

Accepted Answer

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

Question 5

Use a double integral to find the volume of the solid shown in the figure.

Accepted Answer

A) 5,996 
B) 5,994 
C) 6,000 
D) 6,008 
A) 5,996 
B) 5,994 
C) 6,000 
D) 6,008

Question 6

Evaluate the double integral   for the given function f(x, y) and the region R.

Accepted Answer

A) 14 
B) 13 
C) 11 
D) 18 
E) 2 
A) 14 
B) 13 
C) 11 
D) 18 
E) 2

Question 7

Find the maximum and minimum values of the function   subject to the constraint   .

Accepted Answer

A) Maxima :   Minima :
  
B) Maxima :   Minima :
  
C) Maxima :   Minima :
  
D) Maxima :   Minima :
  
A) Maxima :   Minima :
  
B) Maxima :   Minima :
  
C) Maxima :   Minima :
  
D) Maxima :   Minima :

Question 8

Evaluate the double integral   for the given function f(x, y) and the region R.   ; R is bounded by x = 0, x = 1, y = 0 and y = x.

Accepted Answer

The answer of Evaluate the double integral   for...

Question 9

The total daily profit (in dollars) realized by Weston Publishing in publishing and selling its dictionaries is given by the profit function   where x stands for the number of deluxe editions and y denotes the number of standard editions sold daily.Weston's management decides that publication of these dictionaries should be restricted to a total of exactly 400 copies/day.How many deluxe copies and how many standard copies should be published each day to maximize Weston's daily profit?
Find the number of deluxe copies.
Find the number of standard copies.

Accepted Answer

The answer of The total daily profit (in dollars) realized...

Question 10

Evaluate the double integral   for the given function f(x, y) and the region R.
f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x.

Accepted Answer

The answer of Evaluate the double integral   for...

Question 11

Steel has been playing a decreasing role in the manufacture of beverage cans in the United States.The use of bimetallic cans has been dwindling, whereas the use of all-aluminum cans has been growing steadily.The accompanying table gives the production (in billions) of all-aluminum cans over the period from 1975 through 1989:   Find an equation of the least-squares line for these data.(Let x = 1 represent the year 1975.) Please round the coefficients in your equation to three decimal places.Use the result to estimate the number of cans produced in 1993, assuming the trend continued.

Accepted Answer

A) y = 4.834x + 11.857; 103.666 billion cans 
B) y = 4.842x + 11.842; 103.863 billion cans 
C) y = 4.842x + 11.842; 103.840 billion cans 
D) y = 4.834x + 11.857; 103.703 billion cans 
A) y = 4.834x + 11.857; 103.666 billion cans 
B) y = 4.842x + 11.842; 103.863 billion cans 
C) y = 4.842x + 11.842; 103.840 billion cans 
D) y = 4.834x + 11.857; 103.703 billion cans

Question 12

The Ross-Simons Company has a monthly advertising budget of $40,000.Their marketing department estimates that if they spend x dollars on newspaper advertising and y dollars on television advertising, then the monthly sales will be given by   dollars.Determine how much money Ross-Simons should spend on newspaper ads and on television ads each month to maximize its monthly sales.

Accepted Answer

A) $31,000 on newspaper advertisements and $11,000 on television advertisements 
B) $28,000 on newspaper advertisements and $8,000 on television advertisements 
C) $33,000 on newspaper advertisements and $13,000 on television advertisements 
D) $30,000 on newspaper advertisements and $10,000 on television advertisements 
A) $31,000 on newspaper advertisements and $11,000 on television advertisements 
B) $28,000 on newspaper advertisements and $8,000 on television advertisements 
C) $33,000 on newspaper advertisements and $13,000 on television advertisements 
D) $30,000 on newspaper advertisements and $10,000 on television advertisements

Question 13

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 105 in.Find the dimensions of the cylindrical package of greatest volume that may be sent through the mail.What is the volume of such a package? Hint: The length plus the girth is   , and the volume is   .

Accepted Answer

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

Question 14

An open rectangular box having a surface area of     is to be constructed from a tin sheet.Find the diamensions of the box if the volume of the box is to be as large as possible.What is the maximum volume? Hint : Let the diamentions of the box be   (see the figure as follows).Then the surface area is   and its volume is   .

Accepted Answer

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

Question 15

The total daily revenue (in dollars) that Weston Publishing realizes in publishing and selling its English-language dictionaries is given by   where x denotes the number of deluxe copies and y denotes the number of standard copies published and sold daily.The total daily cost of publishing these dictionaries is given by   dollars.Determine how many deluxe copies and how many standard copies Weston should publish each day to maximize its profits.Please round the answers to the nearest integer.
__________ deluxe copies
__________ standard copies
What is the maximum profit realizable? Please round the answer to the nearest dollar.
$__________

Accepted Answer

The answer of The total daily revenue (in dollars) that...

Question 16

Find the volume of the solid bounded above by the surface
z = f(x, y)
and below by the plane region R.   ; R is the region bounded by   .

Accepted Answer

The answer of Find the volume of the solid bounded...

Question 17

The spending (in billions of dollars) by Medicaid, the national health-care plan for the poor, over the 5-year period from 1988 to 1992 is summarized in the following table.   (Here, x = 0 represents the beginning of the year 1988.) Find an equation of the least-squares line for these data.Please round the coefficients in your equation to three decimal places.Use the result of to estimate Medicaid spending in Massachusetts for the year 2001, assuming the trend continued.

Accepted Answer

A) y = 0.113x + 1.546; $3.015 billion 
B) y = 0.114x + 1.550; $3.004 billion 
C) y = 0.114x + 1.550; $3.032 billion 
D) y = 0.113x + 1.546; $2.959 billion 
A) y = 0.113x + 1.546; $3.015 billion 
B) y = 0.114x + 1.550; $3.004 billion 
C) y = 0.114x + 1.550; $3.032 billion 
D) y = 0.113x + 1.546; $2.959 billion

Question 18

Find the domain of the function. f(m, n) = 2m + 9n

Accepted Answer

A) All real values of m and n satisfying 2m + 9n > 0 B) All real values of m and n satisfying 2m + 9n < 0 C) All real values of m and n A) All real values of m and n satisfying 2m + 9n > 0 B) All real values of m and n satisfying 2m + 9n < 0 C) All real values of m and n

Question 19

Find the volume of the solid bounded above by the surface   and below by the plane region   .   and   is the region bounded by the graphs of   and   .

Accepted Answer

The answer of Find the volume of the solid bounded...

Question 20

Let   Compute the following.
f(1, 2) = __________
f(2, 1) = __________
f(- 1, 2) = __________
f(2, - 1) = __________

Accepted Answer

The answer of Let   Compute the following.
f(1, 2)...

Let Compute the following. g(1, 1, 1), g(- 1, 0, 1), g(- 1, 1, 1)

Let Compute the following. f(1, 2), f(2, - 1)

Maximize the function subject to the constraint .

If is a function of x and y, then there are functions and of one variable such a that

Use a double integral to find the volume of the solid shown in the figure.

Evaluate the double integral for the given function f(x, y) and the region R.

Find the maximum and minimum values of the function subject to the constraint .

Evaluate the double integral for the given function f(x, y) and the region R. ; R is bounded by x = 0, x = 1, y = 0 and y = x.

Evaluate the double integral for the given function f(x, y) and the region R. f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x.

Find the volume of the solid bounded above by the surface z = f(x, y) and below by the plane region R. ; R is the region bounded by .

Find the domain of the function. f(m, n) = 2m + 9n

Find the volume of the solid bounded above by the surface and below by the plane region . and is the region bounded by the graphs of and .

Let Compute the following. f(1, 2) = f(2, 1) = f(- 1, 2) = f(2, - 1) =

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Filters

Exam 8: Calculus of Several Variables

Let Compute the following. g(1, 1, 1), g(- 1, 0, 1), g(- 1, 1, 1)

Let Compute the following. f(1, 2), f(2, - 1)

Maximize the function subject to the constraint .

If is a function of x and y, then there are functions and of one variable such a that

Use a double integral to find the volume of the solid shown in the figure.

Evaluate the double integral for the given function f(x, y) and the region R.

Find the maximum and minimum values of the function subject to the constraint .

Evaluate the double integral for the given function f(x, y) and the region R. ; R is bounded by x = 0, x = 1, y = 0 and y = x.

Evaluate the double integral for the given function f(x, y) and the region R. f(x, y) = 3x + 4y; R is bounded by x = 0, x = 1, y = 0 and y = x.

Find the volume of the solid bounded above by the surface z = f(x, y) and below by the plane region R. ; R is the region bounded by .

Find the domain of the function. f(m, n) = 2m + 9n

Find the volume of the solid bounded above by the surface and below by the plane region . and is the region bounded by the graphs of and .

Let Compute the following. f(1, 2) = __________ f(2, 1) = __________ f(- 1, 2) = __________ f(2, - 1) = __________

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Filters

Let Compute the following. f(1, 2) = f(2, 1) = f(- 1, 2) = f(2, - 1) =