Question 1

Evaluate the integral   . ​

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Question 2

Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by   , where t is the number of years past 1960. Find the total personal income in 2016 by using the arbitrary constant that is evaluated by using the data point from 1960. Also find the rate of change of total personal income in 2016. Round your answers to two decimal places. ​   ​

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Question 3

Evaluate the integral   . ​

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Question 4

Use algebra to rewrite the integrand; then integrate and simplify. ​   ​

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Question 5

Evaluate the integral   . ​

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Question 6

Evaluate the integral   . ​

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Question 7

Evaluate the integral   . ​

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Question 8

Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by   , where t is the number of years past 1960. The value of   are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret   . Round your answer to two decimal places, if necessary. ​

Accepted Answer

A)   
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year. 
B)   
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year. 
C)   
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year. 
D)   
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month. 
E)   
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month. 
A)   
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year. 
B)   
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year. 
C)   
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year. 
D)   
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month. 
E)   
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.

Question 9

A family of functions is given below. Find the function f (x) such that the family is given by   . ​   ​

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Question 10

Find the general solution of the differential equation   . ​

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Question 11

Evaluate the integral   . ​

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Question 12

Use integration to find the general solution to the differential equation   . ​

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Question 13

Given the functions below, decide which function is f (x), and which is a member of the family   . ​   ​

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A)   
And  
Is a member of the family of   
B)   
And  
Is a member of the family of   
C)   
And  
Is a member of the family of   
D)   
And  
Is a member of the family of   
E)   
And  
Is a member of the family of   
A)   
And  
Is a member of the family of   
B)   
And  
Is a member of the family of   
C)   
And  
Is a member of the family of   
D)   
And  
Is a member of the family of   
E)   
And  
Is a member of the family of

Question 14

Find the particular solution to the given differential equation. ​   , when   ​

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Question 15

Suppose that the rate at which blood pressure decreases in the aorta of a normal adult after a heartbeat is   ,where t is the time in seconds. Use the function that describes the blood pressure in the aorta if   when   to find the blood pressure 0.9 second after a heartbeat. Round your answer to two decimal places. ​

Accepted Answer

A) ​44.24 
B) 169.06 
C) 36.68 
D) 37.98 
E) 42.74 
A) ​44.24 
B) 169.06 
C) 36.68 
D) 37.98 
E) 42.74

Question 16

Find du if   . ​

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Question 17

Suppose that the marginal revenue for a product is   and the marginal cost is   with a fixed cost of $900. How many units will result in a maximum profit? ​

Accepted Answer

A) 9 units 
B) 8 units 
C) 7 units 
D) 11 units 
E) 10 units 
A) 9 units 
B) 8 units 
C) 7 units 
D) 11 units 
E) 10 units

Question 18

Evaluate the integral   . ​

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Question 19

Evaluate the integral   . ​

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Question 20

The rate of production of a new line of products is given by   , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that   when   , find the total number of items produced as a function of time t. ​

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Evaluate the integral .

Evaluate the integral .

Use algebra to rewrite the integrand; then integrate and simplify.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

A family of functions is given below. Find the function f (x) such that the family is given by .

Find the general solution of the differential equation .

Evaluate the integral .

Use integration to find the general solution to the differential equation .

Given the functions below, decide which function is f (x), and which is a member of the family .

Find the particular solution to the given differential equation. , when

Find du if .

Suppose that the marginal revenue for a product is and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit?

Evaluate the integral .

Evaluate the integral .

The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t.

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 13: Indefinite Integrals

Evaluate the integral . ​

Evaluate the integral . ​

Use algebra to rewrite the integrand; then integrate and simplify. ​ ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

A family of functions is given below. Find the function f (x) such that the family is given by . ​ ​

Find the general solution of the differential equation . ​

Evaluate the integral . ​

Use integration to find the general solution to the differential equation . ​

Given the functions below, decide which function is f (x), and which is a member of the family . ​ ​

Find the particular solution to the given differential equation. ​ , when ​

Find du if . ​

Suppose that the marginal revenue for a product is and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit? ​

Evaluate the integral . ​

Evaluate the integral . ​

The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t. ​

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Evaluate the integral .

Evaluate the integral .

Use algebra to rewrite the integrand; then integrate and simplify.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

A family of functions is given below. Find the function f (x) such that the family is given by .

Find the general solution of the differential equation .

Evaluate the integral .

Use integration to find the general solution to the differential equation .

Given the functions below, decide which function is f (x), and which is a member of the family .

Find the particular solution to the given differential equation. , when

Find du if .

Suppose that the marginal revenue for a product is and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit?

Evaluate the integral .

Evaluate the integral .

The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t.