Question 1

Evaluate the integral   . ​

Accepted Answer

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

Question 2

Evaluate the integral   . ​

Accepted Answer

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

Question 3

True or false. For the function   gives the area between the graph of   and the x-axis from   .
​

Accepted Answer

A) True 
 B)False

Question 4

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by   , where   represents 1990. Evaluate   . Round your answer to the nearest cent. ​

Accepted Answer

A)  $1,358.51 
B)  $15,558.45 
C)  $93,350.70 
D)  $10,372.30 
E)  $51,861.50 
A)  $1,358.51 
B)  $15,558.45 
C)  $93,350.70 
D)  $10,372.30 
E)  $51,861.50

Question 5

Evaluate the given integral with the Fundamental Theorem of Calculus   . ​

Accepted Answer

A)  -26 
B)  -25 
C)  -28 
D)  -35 
E)  -31 
A)  -26 
B)  -25 
C)  -28 
D)  -35 
E)  -31

Question 6

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by   (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by   . ​

Accepted Answer

A)  $107,619.44 
B)  $247,524.72 
C)  $63,305.55 
D)  $333,620.27 
E)  $150,667.22 
A)  $107,619.44 
B)  $247,524.72 
C)  $63,305.55 
D)  $333,620.27 
E)  $150,667.22

Question 7

Suppose that a printing firm considers the production of its presses as a continuous income stream. If the annual rate of flow at time t is given by   in thousands of dollars per year, and if money is worth 7% compounded continuously, find the present value and future value of the presses over the next 10 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424 
A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424

Question 8

Suppose that a vending machine company is considering selling some of its machines. Suppose further that the income from these particular machines is a continuous stream with an annual rate of flow at time t given by   Find the present value and future value of the machines over the next 3 years if the money is worth 11% compounded continuously. Round answers to the nearest dollar. ​

Accepted Answer

A)  PV = $1,893
FV = $2,633 
B)  ​PV = $1,893
FV = $2,349 
C)  PV = $1,689
FV = $2,349 
D)  PV = $1,689
FV = $2,633 
E)  PV = $2,364
FV = $2,633 
A)  PV = $1,893
FV = $2,633 
B)  ​PV = $1,893
FV = $2,349 
C)  PV = $1,689
FV = $2,349 
D)  PV = $1,689
FV = $2,633 
E)  PV = $2,364
FV = $2,633

Question 9

Evaluate the integral   . ​

Accepted Answer

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

Question 10

Evaluate the integral   .

Accepted Answer

A)  0 
B)    
C)    
D)    
E)  integral diverges 
A)  0 
B)    
C)    
D)    
E)  integral diverges

Question 11

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 12

Evaluate the integral   . ​

Accepted Answer

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

Question 13

Use integration by parts to evaluate the integral   . Note that evaluation may require integration by parts more than once. ​

Accepted Answer

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

Question 14

Evaluate the improper integral if it converges, or state that it diverges. ​   ​

Accepted Answer

A)    
B)  ​   
C)    
D)    
E)  diverges 
A)    
B)  ​   
C)    
D)    
E)  diverges

Question 15

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function   . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Accepted Answer

A)  0.242 
B)  0.567 
C)  0.391 
D)  0.758 
E)  0.609 
A)  0.242 
B)  0.567 
C)  0.391 
D)  0.758 
E)  0.609

Question 16

If the demand function for a product is   and the supply function is   where p is in millions of dollars and x is the number of thousands of units. Find the consumer's surplus. Round your answer to the nearest million dollars. ​​

Accepted Answer

A)  ​270 million dollars 
B)  ​267 million dollars 
C)  ​257 million dollars 
D)  ​181 million dollars 
E)  ​219 million dollars 
A)  ​270 million dollars 
B)  ​267 million dollars 
C)  ​257 million dollars 
D)  ​181 million dollars 
E)  ​219 million dollars

Question 17

The total cost function for a product is   , and the demand function is   , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent. ​

Accepted Answer

A)  $256.00 
B)  $295.38 
C)  $576.00 
D)  $384.00 
E)  $182.86 
A)  $256.00 
B)  $295.38 
C)  $576.00 
D)  $384.00 
E)  $182.86

Question 18

Evaluate the improper integral if it converges, or state that it diverges. ​

Accepted Answer

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

Question 19

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by   (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent. ​

Accepted Answer

A)  $165,371.54 
B)  $142,489.95 
C)  $391,947.09 
D)  $226,559.01 
E)  $159,548.60 
A)  $165,371.54 
B)  $142,489.95 
C)  $391,947.09 
D)  $226,559.01 
E)  $159,548.60

Question 20

For the interval [3,15] and n = 4, find the values of   ​

Accepted Answer

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

Evaluate the integral .

Evaluate the integral .

True or false. For the function gives the area between the graph of and the x-axis from .

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent.

Evaluate the given integral with the Fundamental Theorem of Calculus .

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

Evaluate the integral .

Evaluate the integral .

Use an integral formula to evaluate .

Evaluate the integral .

Use integration by parts to evaluate the integral . Note that evaluation may require integration by parts more than once.

Evaluate the improper integral if it converges, or state that it diverges.

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

If the demand function for a product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the consumer's surplus. Round your answer to the nearest million dollars.

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent.

Evaluate the improper integral if it converges, or state that it diverges.

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent.

For the interval [3,15] and n = 4, find the values of

Linear Equations and Functions

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Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

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Indefinite Integrals

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Exam 13: A: Definite Integrals - Techniques

Evaluate the integral . ​

Evaluate the integral . ​

True or false. For the function gives the area between the graph of and the x-axis from . ​

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent. ​

Evaluate the given integral with the Fundamental Theorem of Calculus . ​

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by . ​

Evaluate the integral . ​

Evaluate the integral .

Use an integral formula to evaluate . ​

Evaluate the integral . ​

Use integration by parts to evaluate the integral . Note that evaluation may require integration by parts more than once. ​

Evaluate the improper integral if it converges, or state that it diverges. ​ ​

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

If the demand function for a product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the consumer's surplus. Round your answer to the nearest million dollars. ​​

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent. ​

Evaluate the improper integral if it converges, or state that it diverges. ​

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent. ​

For the interval [3,15] and n = 4, find the values of ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

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Evaluate the integral .

Evaluate the integral .

True or false. For the function gives the area between the graph of and the x-axis from .

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent.

Evaluate the given integral with the Fundamental Theorem of Calculus .

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

Evaluate the integral .

Use an integral formula to evaluate .

Evaluate the integral .

Use integration by parts to evaluate the integral . Note that evaluation may require integration by parts more than once.

Evaluate the improper integral if it converges, or state that it diverges.

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

If the demand function for a product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the consumer's surplus. Round your answer to the nearest million dollars.

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent.

Evaluate the improper integral if it converges, or state that it diverges.

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent.

For the interval [3,15] and n = 4, find the values of