Question 1

Find the average value of the function   ​

Accepted Answer

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

Question 2

Use the table values and apply the Simpson's Rule to approximate   to one decimal place.

Accepted Answer

A)  1.7 
B)  1.6 
C)  1.3 
D)  2.0 
E)  2.3 
A)  1.7 
B)  1.6 
C)  1.3 
D)  2.0 
E)  2.3

Question 3

Suppose the Lorenz curve for the distribution of income of a certain country is given by   Find the Gini coefficient of income. Round your answer to three decimal places. ​

Accepted Answer

A)  2.632 
B)  2.896 
C)  4.264 
D)  5.632 
E)  0.264 
A)  2.632 
B)  2.896 
C)  4.264 
D)  5.632 
E)  0.264

Question 4

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by   in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $712,660 
B)  $716,213 
C)  $703,158 
D)  $722,162 
E)  $708,733 
A)  $712,660 
B)  $716,213 
C)  $703,158 
D)  $722,162 
E)  $708,733

Question 5

Use the function   from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

Accepted Answer

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

Question 6

Suppose that the profit from a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by   (dollars per year). If money is worth 14%, compounded continuously, find the present value of this stream over the next 5 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $26,730 
B)  $52,226 
C)  $35,579 
D)  $28,485 
E)  $39,326 
A)  $26,730 
B)  $52,226 
C)  $35,579 
D)  $28,485 
E)  $39,326

Question 7

Suppose that the output of the machinery in a factory can be considered as a continuous income stream with an annual rate of flow at time t given by   in thousands of dollars per year. If the annual interest rate is 4% compounded continuously, find the capital value of the machinery. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $4,406,250 
B)  $1,175,000 
C)  $1,958,333 
D)  $6,462,500 
E)  $2,937,500 
A)  $4,406,250 
B)  $1,175,000 
C)  $1,958,333 
D)  $6,462,500 
E)  $2,937,500

Question 8

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 9

Find the producer's surplus for a product with demand function   and supply function   where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​

Accepted Answer

A)  37.5 million dollars 
B)  26.5 million dollars 
C)  21.0 million dollars 
D)  22.5 million dollars 
E)  23.5 million dollars 
A)  37.5 million dollars 
B)  26.5 million dollars 
C)  21.0 million dollars 
D)  22.5 million dollars 
E)  23.5 million dollars

Question 10

Suppose the marginal cost for x units of a good is   (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar. ​

Accepted Answer

A)  168 dollars 
B)  226 dollars 
C)  228 dollars 
D)  170 dollars 
E)  240 dollars 
A)  168 dollars 
B)  226 dollars 
C)  228 dollars 
D)  170 dollars 
E)  240 dollars

Question 11

Use the sum formulas to find the value of the sum that follows. ​   ​

Accepted Answer

A)  720 
B)  160 
C)  435 
D)  820 
E)  90 
A)  720 
B)  160 
C)  435 
D)  820 
E)  90

Question 12

Use an integral formula to evaluate   .

Accepted Answer

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

Question 13

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 14

Suppose the presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. The group measures the length across the algae growth (see the figure) and obtains the following data (in feet).  
​
Use 8 rectangles with bases of 10 feet and lengths measured at the left-hand endpoints to approximate the area of the algae growth.   ​
​

Accepted Answer

A)  1,730 sq ft 
B)  1,704 sq ft 
C)  2,076 sq ft 
D)  2,520 sq ft 
E)  2,556 sq ft 
A)  1,730 sq ft 
B)  1,704 sq ft 
C)  2,076 sq ft 
D)  2,520 sq ft 
E)  2,556 sq ft

Question 15

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by   where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year. ​

Accepted Answer

A)  120 years 
B)  137 years 
C)  84 years 
D)  270 years 
E)  47 years 
A)  120 years 
B)  137 years 
C)  84 years 
D)  270 years 
E)  47 years

Question 16

The supply function for a good is   , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Accepted Answer

A)  $88.40 
B)  $40.00 
C)  $28.89 
D)  $78.00 
E)  $52.00 
A)  $88.40 
B)  $40.00 
C)  $28.89 
D)  $78.00 
E)  $52.00

Question 17

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 18

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 19

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 20

Evaluate   . ​

Accepted Answer

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

Find the average value of the function

Use the table values and apply the Simpson's Rule to approximate to one decimal place.

Suppose the Lorenz curve for the distribution of income of a certain country is given by Find the Gini coefficient of income. Round your answer to three decimal places.

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar.

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

Use an integral formula to evaluate .

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar.

Use the sum formulas to find the value of the sum that follows.

Use an integral formula to evaluate .

Use an integral formula to evaluate .

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year.

The supply function for a good is , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

Use integration by parts to evaluate .

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.

Evaluate .

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Derivatives

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Exam 13: A: Definite Integrals - Techniques

Find the average value of the function ​

Use the table values and apply the Simpson's Rule to approximate to one decimal place.

Suppose the Lorenz curve for the distribution of income of a certain country is given by Find the Gini coefficient of income. Round your answer to three decimal places. ​

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar. ​

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

Use an integral formula to evaluate . ​

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar. ​

Use the sum formulas to find the value of the sum that follows. ​ ​

Use an integral formula to evaluate .

Use an integral formula to evaluate . ​

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year. ​

The supply function for a good is , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Use integration by parts to evaluate . ​

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. ​ ​ ​

Evaluate . ​

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

Filters

Find the average value of the function

Suppose the Lorenz curve for the distribution of income of a certain country is given by Find the Gini coefficient of income. Round your answer to three decimal places.

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar.

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

Use an integral formula to evaluate .

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar.

Use the sum formulas to find the value of the sum that follows.

Use an integral formula to evaluate .

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year.

The supply function for a good is , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

Use integration by parts to evaluate .

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.

Evaluate .