Question 1

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 2

Use rectangles to find the area between   and the x-axis from   to   ​

Accepted Answer

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

Question 3

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 4

Use Simpson's Rule to approximate   with n = 6. Round your answer to two decimal places. ​

Accepted Answer

A)  49.11 
B)  98.00 
C)  261.78 
D)  86.89 
E)  260.00 
A)  49.11 
B)  98.00 
C)  261.78 
D)  86.89 
E)  260.00

Question 5

Equations are given whose graphs enclose a region. Find the area of the region. ​

Accepted Answer

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

Question 6

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 7

Suppose that the rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up, and the following data are obtained. Use the Trapezoidal Rule to approximate the total number of units produced in the first 5 weeks. Round your answer to two decimal places.

Accepted Answer

A)  1,323.15 units 
B)  2100.30 units 
C)  573.83 units 
D)  1667.90 units 
E)  833.60 units 
A)  1,323.15 units 
B)  2100.30 units 
C)  573.83 units 
D)  1667.90 units 
E)  833.60 units

Question 8

Find the value of the sum   ​

Accepted Answer

A)  8,784 
B)  8,808 
C)  5,675 
D)  8,800 
E)  2,622 
A)  8,784 
B)  8,808 
C)  5,675 
D)  8,800 
E)  2,622

Question 9

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the left-hand endpoints of the subintervals. Compute the approximate area using up to 4 decimal places as needed. ​   from   to     subintervals.
​

Accepted Answer

A)  11.625 square units 
B)  23.25 square units 
C)  19.25 square units 
D)  46.5 square units 
E)  2 square units 
A)  11.625 square units 
B)  23.25 square units 
C)  19.25 square units 
D)  46.5 square units 
E)  2 square units

Question 10

If the supply function for x units of a commodity is   dollars, what is the producer's surplus at   ? Round your answer to two decimal places. ​

Accepted Answer

A)  $3,576.9 
B)  $2,928.14 
C)  $25,657.84 
D)  $3,056.14 
E)  $25,785.84 
A)  $3,576.9 
B)  $2,928.14 
C)  $25,657.84 
D)  $3,056.14 
E)  $25,785.84

Question 11

When the area under   from   to   is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: ​
Left-hand endpoints:   ​
Right-hand endpoints:   ​
Find   ​

Accepted Answer

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

Question 12

The demand function for a product is   , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus? ​

Accepted Answer

A)  $1,175 
B)  $1,250 
C)  $1,375 
D)  $1,220 
E)  $1,340 
A)  $1,175 
B)  $1,250 
C)  $1,375 
D)  $1,220 
E)  $1,340

Question 13

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​
I. Integration by parts 
II.  
III.  
IV.  
  ​

Accepted Answer

A)  I. Integration by parts;   
B)    
C)    
D)  ​   
E)  not integrable by any of the techniques we have studied 
A)  I. Integration by parts;   
B)    
C)    
D)  ​   
E)  not integrable by any of the techniques we have studied

Question 14

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function   where   represents 1995. Use   equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between   and   . Round your answer to one decimal place. ​

Accepted Answer

A)  1,079.1 billion dollars 
B)  506.5 billion dollars 
C)  575.3 billion dollars 
D)  440.9 billion dollars 
E)  539.5 billion dollars 
A)  1,079.1 billion dollars 
B)  506.5 billion dollars 
C)  575.3 billion dollars 
D)  440.9 billion dollars 
E)  539.5 billion dollars

Question 15

Evaluate the definite integral   . ​

Accepted Answer

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

Question 16

Evaluate the integral   . ​

Accepted Answer

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

Question 17

Find the area of the shaded region for the graph given below.

Accepted Answer

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

Question 18

If the marginal cost function for x units of a product is   dollars per unit, and if the fixed cost is $120, find the total cost function. ​

Accepted Answer

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

Question 19

If the supply function for a commodity is   where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars. ​

Accepted Answer

A)  5,623 million dollars 
B)  3,461 million dollars 
C)  3,468 million dollars 
D)  3,999 million dollars 
E)  3,524 million dollars 
A)  5,623 million dollars 
B)  3,461 million dollars 
C)  3,468 million dollars 
D)  3,999 million dollars 
E)  3,524 million dollars

Question 20

The probability density function for the life span of an electronics part is   where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places. ​

Accepted Answer

A)  0.487 
B)  0.513 
C)  0.532 
D)  0.497 
E)  0.468 
A)  0.487 
B)  0.513 
C)  0.532 
D)  0.497 
E)  0.468

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

Use rectangles to find the area between and the x-axis from to

Use Simpson's Rule to approximate with n = 6. Round your answer to two decimal places.

Equations are given whose graphs enclose a region. Find the area of the region.

Find the value of the sum

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the left-hand endpoints of the subintervals. Compute the approximate area using up to 4 decimal places as needed. from to subintervals.

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to two decimal places.

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: Left-hand endpoints: Right-hand endpoints: Find

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus?

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. I. Integration by parts II. III. IV.

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place.

Evaluate the definite integral .

Evaluate the integral .

Find the area of the shaded region for the graph given below.

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $120, find the total cost function.

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars.

The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places.

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

Exam 13: A: Definite Integrals - Techniques

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

Use rectangles to find the area between and the x-axis from to ​

Use Simpson's Rule to approximate with n = 6. Round your answer to two decimal places. ​

Equations are given whose graphs enclose a region. Find the area of the region. ​

Find the value of the sum ​

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to two decimal places. ​

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: ​ Left-hand endpoints: ​ Right-hand endpoints: ​ Find ​

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus? ​

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​ I. Integration by parts II. III. IV. ​

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place. ​

Evaluate the definite integral . ​

Evaluate the integral . ​

Find the area of the shaded region for the graph given below.

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $120, find the total cost function. ​

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars. ​

The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places. ​

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

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

Use rectangles to find the area between and the x-axis from to

Use Simpson's Rule to approximate with n = 6. Round your answer to two decimal places.

Equations are given whose graphs enclose a region. Find the area of the region.

Find the value of the sum

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to two decimal places.

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: Left-hand endpoints: Right-hand endpoints: Find

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus?

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. I. Integration by parts II. III. IV.

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place.

Evaluate the definite integral .

Evaluate the integral .

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $120, find the total cost function.

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars.

The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places.