Question 1

Find the first partial derivatives of the function.

Accepted Answer

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

Question 2

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 3

Maximize the function   subject to the constraint   .

Accepted Answer

The answer of Maximize the function   subject to...

Question 4

In a survey it was determined that the demand equation for VCRs is given by   The demand equation for blank VCR tapes is given by   where   and   denote the unit prices, respectively, and   and   denote the number of VCRs and the number of blank VCR tapes demanded each week. Determine whether these two products are substitute, complementary, or neither.

Accepted Answer

The answer of In a survey it was determined that...

Question 5

Evaluate the double integral   for the function   and the region   .   and   is the rectangle defined by   and   .

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

The answer of The Ross-Simons Company has a monthly advertising...

Question 8

The Company requires that its corned beef hash containers have a capacity of   , be right circular cylinders, and be made of a tin alloy. Find the radius and height of the least expensive container that can be made if the metal for the side and bottom costs   and the metal for the pull-off lid costs   .

Accepted Answer

The answer of The Company requires that its corned beef...

Question 9

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

Question 10

An auxiliary electric power station will serve three communities, A, B, and C, whose relative locations are shown in the accompanying figure. Determine where the power station should be located if the sum of the squares of the distances from each community to the site is minimized. Please round the answer to the nearest hundredth.

Accepted Answer

The answer of An auxiliary electric power station will serve...

Question 11

Find the domain of the function.
f(m, n) = 2m + 4n

Accepted Answer

All real v

Question 12

Maximize the function   subject to the constraints   .

Accepted Answer

A)  Max. of   at
  
B)  Max. of   at
  
C)  Max. of   at
  
D)  Max. of   at
  
E)  Max. of   at
  
A)  Max. of   at
  
B)  Max. of   at
  
C)  Max. of   at
  
D)  Max. of   at
  
E)  Max. of   at

Question 13

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

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

Question 14

Find the second-order partial derivatives of the given function. Show that the mixed partial derivatives   and   are equal.

Accepted Answer

A)

B)

C)

D)

A)

B)

C)

D)

Question 15

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 16

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 17

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function.   Find the critical point(s) of the function.
Find the point(s) of maximum.
Find the point(s) of minimum.
Find the relative extrema of the function.

Accepted Answer

The answer of Find the critical point(s) of the function....

Question 18

The total weekly revenue (in dollars) of Country Workshop associated with manufacturing and selling their rolltop desks is given by the function   where x denotes the number of finished units and y denotes the number of unfinished units manufactured and sold each week. Compute   and   when x = 200 and y = 180. Interpret your results.

Accepted Answer

A)  $36/unit; $24/unit The weekly revenue increases by $36/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue increases by $24/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
B)  - $380/unit; - $20/unit The weekly revenue decreases by $380/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue decreases by $20/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
C)  $36/unit; - $24/unit The weekly revenue increases by $36/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue decreases by $24/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
D)  $24/unit; $36/unit The weekly revenue increases by $36/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue decreases by $24/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
A)  $36/unit; $24/unit The weekly revenue increases by $36/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue increases by $24/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
B)  - $380/unit; - $20/unit The weekly revenue decreases by $380/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue decreases by $20/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
C)  $36/unit; - $24/unit The weekly revenue increases by $36/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue decreases by $24/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200. 
D)  $24/unit; $36/unit The weekly revenue increases by $36/unit for each additional finished desk produced (beyond 200) when the level of production of unfinished desks remains fixed at 180; the revenue decreases by $24/unit when each additional unfinished desk (beyond 180) is produced and the level of production of finished desks remains fixed at 200.

Question 19

Body mass index (BMI) is used to identify, evaluate, and treat overweight and obese adults. The BMI value for an adult of weight   (in kilograms) and height   (in meters) is defined to be   According to federal guidlines, an adult is overweight iff he or she has a BMI value greater than 25 but less than 30 and is "obese" if the value greater than or equal to 30. What is the BMI of adult who weights in at 80 kg and stands 1.7 m tall?
Round your answers to two decimal places if necessary.

Accepted Answer

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

Question 20

With computer security always a hot-button issue, demand is growing for technology that authenticates and authorizes computer users. The following table gives the authentication software sales (in billions of dollars), including projections, from 1999 through 2004.   (Here, x = 0 represents 1999.)
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 to estimate the sales for 2006, assuming the projection is accurate.

Accepted Answer

A)  y = 0.759x + 2.273; $7.586 billion 
B)  y = 0.749x + 2.262; $7.482 billion 
C)  y = 0.759x + 2.273; $7.549 billion 
D)  y = 0.749x + 2.262; $7.505 billion 
A)  y = 0.759x + 2.273; $7.586 billion 
B)  y = 0.749x + 2.262; $7.482 billion 
C)  y = 0.759x + 2.273; $7.549 billion 
D)  y = 0.749x + 2.262; $7.505 billion

Find the first partial derivatives of the function.

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 .

Maximize the function subject to the constraint .

Evaluate the double integral for the function and the region . and is the rectangle defined by and .

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

The Company requires that its corned beef hash containers have a capacity of , be right circular cylinders, and be made of a tin alloy. Find the radius and height of the least expensive container that can be made if the metal for the side and bottom costs and the metal for the pull-off lid costs .

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

Find the domain of the function. f(m, n) = 2m + 4n

Maximize the function subject to the constraints .

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 .

Find the second-order partial derivatives of the given function. Show that the mixed partial derivatives and are equal.

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

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

Find the first partial derivatives of the function.

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 .

Maximize the function subject to the constraint .

Evaluate the double integral for the function and the region . and is the rectangle defined by and .

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

The Company requires that its corned beef hash containers have a capacity of , be right circular cylinders, and be made of a tin alloy. Find the radius and height of the least expensive container that can be made if the metal for the side and bottom costs and the metal for the pull-off lid costs .

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

Find the domain of the function. f(m, n) = 2m + 4n

Maximize the function subject to the constraints .

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 .

Find the second-order partial derivatives of the given function. Show that the mixed partial derivatives and are equal.

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

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Filters