Question 1

Graph the function.

Accepted Answer

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

Question 2

Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive then more people will buy the other. If p 1 is the price per pair of the Ultra Mini and p 2 is the price of the Big Stack, demand for the Ultra Mini is given by   where q 1 represents the number of pairs of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by   Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Round your answer to the nearest dollar.

Accepted Answer

A) $631 for Ultra Mini and $1,313 for Big Stack 
B) $646 for Ultra Mini and $1,260 for Big Stack 
C) $1,313 for Ultra Mini and $631 for Big Stack 
D) $1,260 for Ultra Mini and $646 for Big Stack 
E) $1,413 for Ultra Mini and $631 for Big Stack 
A) $631 for Ultra Mini and $1,313 for Big Stack 
B) $646 for Ultra Mini and $1,260 for Big Stack 
C) $1,313 for Ultra Mini and $631 for Big Stack 
D) $1,260 for Ultra Mini and $646 for Big Stack 
E) $1,413 for Ultra Mini and $631 for Big Stack

Question 3

Compute the integral.

Accepted Answer

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

Question 4

In the table below, classify each highlighted value.

Accepted Answer

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

Question 5

A productivity model at the Handy Gadget Company is   where P is the number of gadgets the company turns out per month, x is the number of employees at the company, and y is the monthly operating budget in thousands of dollars. Because the company hires part - time workers, it uses anywhere between 50 and 60 workers each month, and its operating budget varies from $8,000 to $14,000 per month. What is the average of the possible numbers gadgets it can turn out per month? (Round the answer to the nearest 1,000 gadgets.)

Accepted Answer

A) 2100 gadgets 
B) 4,16800 gadgets 
C) 4,168000 gadgets 
D) 142000 gadgets 
E) 178000 gadgets 
A) 2100 gadgets 
B) 4,16800 gadgets 
C) 4,168000 gadgets 
D) 142000 gadgets 
E) 178000 gadgets

Question 6

Match between columns
                        Premises: none
a relative maximum
a relative minimum

Accepted Answer

The Answer of R and P and Q is...

Question 7

Calculate   and evaluate each at   .

Accepted Answer

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

Question 8

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 54 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight? Enter your answer as a number without the units.

Accepted Answer

The answer of Trans World Airlines (TWA)has a rule for...

Question 9

Compute the integral.

Accepted Answer

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

Question 10

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.

Accepted Answer

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 
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 11

Locate the maximum of the function.

Accepted Answer

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

Question 12

Classify the highlighted value in the table.

Accepted Answer

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

Question 13

Use Lagrange Multipliers to solve the given problem. Find the maximum value of   subject to   .

Accepted Answer

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

Question 14

For the function   show the cross section at   .

Accepted Answer

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

Question 15

Match between columns
                        Premises: 11ebfe6a_2cfc_9061_96cc_d76310ffb3f0_TBX8650_11

Accepted Answer

The Answer of 11ebfe6a_2cfc_9063_96cc_d5e2f9105b3e_TBX8650_11 and 11ebfe6a_2cfc_9062_96cc_e57c84b8988b_TBX8650_11 is...

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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  
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 18

Locate the local minimum of the function.

Accepted Answer

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

Question 19

Evaluate   for

Accepted Answer

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

Question 20

How many critical points does the following function have?

Accepted Answer

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

Graph the function.

Compute the integral.

In the table below, classify each highlighted value.

Calculate and evaluate each at .

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 54 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight? Enter your answer as a number without the units.

Compute the integral.

Locate the maximum of the function.

Classify the highlighted value in the table.

Use Lagrange Multipliers to solve the given problem. Find the maximum value of subject to .

For the function show the cross section at .

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

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

Locate the local minimum of the function.

Evaluate for

How many critical points does the following function have?

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Techniques of Differentiation With Applications

Further Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Trigonometric Models

Filters

Exam 8: Functions of Several Variables

Graph the function.

Compute the integral.

In the table below, classify each highlighted value.

Calculate and evaluate each at .

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 54 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight? Enter your answer as a number without the units.

Compute the integral.

Locate the maximum of the function.

Classify the highlighted value in the table.

Use Lagrange Multipliers to solve the given problem. Find the maximum value of subject to .

For the function show the cross section at .

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

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

Locate the local minimum of the function.

Evaluate for

How many critical points does the following function have?

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Techniques of Differentiation With Applications

Further Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Trigonometric Models

Filters