Question 1

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). ​   ​

Accepted Answer

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

Question 2

If the marginal revenue (in dollars per unit) for a month is given by   , find the total revenue from the sale of 150 units to the nearest cent. ​

Accepted Answer

A)  $6,808.98 
B)  $6,807.80 
C)  $6,810.00 
D)  $44.80 
E)  $43.60 
A)  $6,808.98 
B)  $6,807.80 
C)  $6,810.00 
D)  $44.80 
E)  $43.60 C

Question 3

If the marginal cost for a product is   , and the production of 15 units results in a total cost of $615, find the total cost function C.

Accepted Answer

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

Question 4

Evaluate the integral   . ​

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Evaluate the integral   . ​

Accepted Answer

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E)    
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B)    
C)    
D)    
E)

Question 7

If $P is invested for n years at 37% compounded continuously, the rate at which the future value is growing is   . What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary. ​

Accepted Answer

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

Question 8

Evaluate the integral   . ​

Accepted Answer

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

Question 9

A new fast-food firm predicts that the number of franchises for its products will grow at the rate   , where t is the number of years. If there is one franchise   at present   , how many franchises are predicted for 35 years from now? ​

Accepted Answer

A)  1,706 
B)  1,736 
C)  1,721 
D)  1,874 
E)  1,670 
A)  1,706 
B)  1,736 
C)  1,721 
D)  1,874 
E)  1,670

Question 10

Evaluate the integral   . ​

Accepted Answer

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

Question 11

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

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

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 14

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

Accepted Answer

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

Question 15

Write the indefinite integral that gives the family associated with   . ​

Accepted Answer

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

Question 16

If the marginal cost, in dollars, for producing a product is   , with a fixed cost of $800, what will be the cost of producing 30 units? ​

Accepted Answer

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

Question 17

Newton's law of cooling (and warming) states that the rate of change of temperature   of an object is proportional to the temperature difference between the object and its surroundings, where T is the constant temperature of the surroundings. That is,   . Suppose an object at 3°C is placed in a room where the temperature is 25°C. If the temperature of the object is 9°C after 1 hour, how long will it take for the object to reach 14°C? Round your answer to one decimal place. ​

Accepted Answer

A)  2.0 hours 
B)  2.2 hours 
C)  2.5 hours 
D)  2.7 hours 
E)  3.3 hours 
A)  2.0 hours 
B)  2.2 hours 
C)  2.5 hours 
D)  2.7 hours 
E)  3.3 hours

Question 18

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies   . If the initial volume of the tumor is 1.93 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places. ​

Accepted Answer

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

Question 19

Evaluate the integral   . ​

Accepted Answer

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

Question 20

An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by   , where S is the sales in thousands of dollars and t is the time in weeks. Find the function that describes the weekly sales revenue if   thousand dollars when   . ​

Accepted Answer

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

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2).

If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 150 units to the nearest cent.

If the marginal cost for a product is , and the production of 15 units results in a total cost of $615, find the total cost function C.

Evaluate the integral .

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

Evaluate the integral .

If $P is invested for n years at 37% compounded continuously, the rate at which the future value is growing is . What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary.

Evaluate the integral .

A new fast-food firm predicts that the number of franchises for its products will grow at the rate , where t is the number of years. If there is one franchise at present , how many franchises are predicted for 35 years from now?

Evaluate the integral .

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

Evaluate the integral .

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

Write the indefinite integral that gives the family associated with .

If the marginal cost, in dollars, for producing a product is , with a fixed cost of $800, what will be the cost of producing 30 units?

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies . If the initial volume of the tumor is 1.93 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places.

Evaluate the integral .

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

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). ​ ​

If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 150 units to the nearest cent. ​

If the marginal cost for a product is , and the production of 15 units results in a total cost of $615, find the total cost function C.

Evaluate the integral . ​

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

Evaluate the integral . ​

If $P is invested for n years at 37% compounded continuously, the rate at which the future value is growing is . What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary. ​

Evaluate the integral . ​

A new fast-food firm predicts that the number of franchises for its products will grow at the rate , where t is the number of years. If there is one franchise at present , how many franchises are predicted for 35 years from now? ​

Evaluate the integral . ​

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

Evaluate the integral . ​

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

Write the indefinite integral that gives the family associated with . ​

If the marginal cost, in dollars, for producing a product is , with a fixed cost of $800, what will be the cost of producing 30 units? ​

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies . If the initial volume of the tumor is 1.93 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places. ​

Evaluate the integral . ​

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

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2).

If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 150 units to the nearest cent.

Evaluate the integral .

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

Evaluate the integral .

If $P is invested for n years at 37% compounded continuously, the rate at which the future value is growing is . What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary.

Evaluate the integral .

A new fast-food firm predicts that the number of franchises for its products will grow at the rate , where t is the number of years. If there is one franchise at present , how many franchises are predicted for 35 years from now?

Evaluate the integral .

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

Evaluate the integral .

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

Write the indefinite integral that gives the family associated with .

If the marginal cost, in dollars, for producing a product is , with a fixed cost of $800, what will be the cost of producing 30 units?

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies . If the initial volume of the tumor is 1.93 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places.

Evaluate the integral .