Question 1

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

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Question 2

Suppose the rate of change of the expected life span l at birth of people born in the United States can be modeled by   where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places, ​
 
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Question 3

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is   , and if there are 0 action potentials when   , find the formula for P(t). ​

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Question 4

The rate of vocabulary memorization of the average student in a certain foreign language course is given by   , where t is the number of continuous hours of study,   , and v is the number of words. About how many words would the average student memorize in 2 hours? Round your answer to the nearest whole number of words. ​

Accepted Answer

A)  36 words 
B)  38 words 
C)  40 words 
D)  41 words 
E)  43 words 
A)  36 words 
B)  38 words 
C)  40 words 
D)  41 words 
E)  43 words

Question 5

Suppose that the marginal propensity to consume is   (in billions of dollars) and that consumption is $4.75 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Accepted Answer

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Question 6

Evaluate the integral   . ​

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Question 7

Evaluate the integral   . ​

Accepted Answer

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E)  ​

Question 8

Suppose that the marginal revenue (in dollars) from the sale of x units of a product is   . What is the revenue from the sale of 150 units of the product? Round your answer to the nearest cent. ​

Accepted Answer

A)  $8,034.21 
B)  $7,634.21 
C)  $11,585.64 
D)  $8,158.00 
E)  $11,061.64 
A)  $8,034.21 
B)  $7,634.21 
C)  $11,585.64 
D)  $8,158.00 
E)  $11,061.64

Question 9

A certain firm's marginal cost, in dollars, for a product is   , its marginal revenue, in dollars, is   , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $172 loss 
B)  $172 profit 
C)  $820 profit 
D)  $820 loss 
E)  $400 loss 
A)  $172 loss 
B)  $172 profit 
C)  $820 profit 
D)  $820 loss 
E)  $400 loss

Question 10

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

Accepted Answer

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Question 11

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

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Question 12

Evaluate the integral   . ​

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Question 13

Find the general solution to the differential equation   . ​

Accepted Answer

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Question 14

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

Accepted Answer

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Question 15

The rate of change of atmospheric pressure P with respect to the altitude above sea level h is proportional to the pressure. That is,   . Suppose that the pressure at sea level is denoted by   and at 14,000 ft, the pressure is half of what it is at sea level. Find the pressure, as a percent of   at 27,000 ft. ​

Accepted Answer

A)  39.5% 
B)  29.9% 
C)  24.3% 
D)  26.3% 
E)  23.1% 
A)  39.5% 
B)  29.9% 
C)  24.3% 
D)  26.3% 
E)  23.1%

Question 16

Evaluate the integral   . ​

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Question 17

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is,   . If $2,500 is invested at 7%, compounded continuously, what will be the future value of this investment after 12 years? Round to the nearest cent. ​

Accepted Answer

A)  $4,600.00 
B)  $5,776.80 
C)  $5,630.48 
D)  $5,708.32 
E)  $5,790.92 
A)  $4,600.00 
B)  $5,776.80 
C)  $5,630.48 
D)  $5,708.32 
E)  $5,790.92

Question 18

Evaluate the integral   . ​

Accepted Answer

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Question 19

Which of the following integrals cannot be integrated by using the methods studied so far? ​
(a)   ​​
(b)   ​
(c)   ​
(d)   ​
(e)   ​

Accepted Answer

A)  a, b 
B)  a, b, e 
C)  b, c, e 
D)  c, d 
E)  d, e 
A)  a, b 
B)  a, b, e 
C)  b, c, e 
D)  c, d 
E)  d, e

Question 20

Find the general solution of the differential equation   . ​

Accepted Answer

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

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

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t).

Suppose that the marginal propensity to consume is (in billions of dollars) and that consumption is $4.75 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Evaluate the integral .

Evaluate the integral .

Suppose that the marginal revenue (in dollars) from the sale of x units of a product is . What is the revenue from the sale of 150 units of the product? Round your answer to the nearest cent.

A certain firm's marginal cost, in dollars, for a product is , its marginal revenue, in dollars, is , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar.

Find the particular solution to the given differential equation. when

Find the particular solution to the given differential equation. when

Evaluate the integral .

Find the general solution to the differential equation .

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

Evaluate the integral .

Evaluate the integral .

Which of the following integrals cannot be integrated by using the methods studied so far? (a) (b) (c) (d) (e)

Find the general solution of the differential equation .

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

Definite Integrals - Techniques

A: 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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Exam 12: Indefinite Integrals

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

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t). ​

Suppose that the marginal propensity to consume is (in billions of dollars) and that consumption is $4.75 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Evaluate the integral . ​

Evaluate the integral . ​

Suppose that the marginal revenue (in dollars) from the sale of x units of a product is . What is the revenue from the sale of 150 units of the product? Round your answer to the nearest cent. ​

A certain firm's marginal cost, in dollars, for a product is , its marginal revenue, in dollars, is , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar. ​

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

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

Evaluate the integral . ​

Find the general solution to the differential equation . ​

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

Evaluate the integral . ​

Evaluate the integral . ​

Which of the following integrals cannot be integrated by using the methods studied so far? ​ (a) ​​ (b) ​ (c) ​ (d) ​ (e) ​

Find the general solution of the differential equation . ​

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

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

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

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t).

Evaluate the integral .

Evaluate the integral .

Suppose that the marginal revenue (in dollars) from the sale of x units of a product is . What is the revenue from the sale of 150 units of the product? Round your answer to the nearest cent.

A certain firm's marginal cost, in dollars, for a product is , its marginal revenue, in dollars, is , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar.

Find the particular solution to the given differential equation. when

Find the particular solution to the given differential equation. when

Evaluate the integral .

Find the general solution to the differential equation .

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

Evaluate the integral .

Evaluate the integral .

Which of the following integrals cannot be integrated by using the methods studied so far? (a) (b) (c) (d) (e)

Find the general solution of the differential equation .