Question 1

Compute   .

Accepted Answer

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

Question 2

The following graph represents the rate of change of a function f with respect to x; i.e., it is the graph of   , with   . Find a value a to one decimal place such that   and   . If there is no such value, enter "none".

Accepted Answer

The answer of The following graph represents the rate of...

Question 3

A family invests in a snow cone stand that has an annual income of $10,000. If they plan to keep the stand for 10 years and save all of the income in an account earning 4.5% interest, compounded continuously, what will their total savings be?

Accepted Answer

The answer of A family invests in a snow cone...

Question 4

Supply and demand curves for a product are shown in the following figure. Suppose an artificially low price of $300 is imposed. Estimate the total gains from trade now, to the nearest 500 dollars.

Accepted Answer

The answer of Supply and demand curves for a product...

Question 5

Evaluate   .

Accepted Answer

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

Question 6

Find

Accepted Answer

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

Question 7

Find

Accepted Answer

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

Question 8

Find an antiderivative   of   such that   .

Accepted Answer

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

Question 9

Find the indefinite integral   .

Accepted Answer

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

Question 10

From the time a child is born until he is 18, a father plans to set aside $100 times the child's current age each year. Find the present value of this income stream, given an interest rate of 7% compounded continuously. Round to the nearest dollar.

Accepted Answer

The answer of From the time a child is born...

Question 11

Consider   . What is the definite integral obtained after making the substitution   ?

Accepted Answer

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

Question 12

Given the following graph of   and the fact that   , determine whether   is positive or negative.

Accepted Answer

The answer of Given the following graph of  ...

Question 13

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 14

Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

Accepted Answer

The answer of Supply and demand curves for a product...

Question 15

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

Accepted Answer

A) 120 
B) 150 
C) 190 
D) 220 
A) 120 
B) 150 
C) 190 
D) 220

Question 16

The demand curve for a product has equation   , and the supply curve has equation   for   , where q is quantity and p is the price per unit. At an artificially high price of $27, find the quantity consumers are willing to purchase and the quantity producers are willing to supply. Use this information to calculate the producer surplus at this price, to the nearest dollar.

Accepted Answer

The answer of The demand curve for a product has...

Question 17

Find   using integration by substitution.

Accepted Answer

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

Question 18

Evaluate   .

Accepted Answer

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

Question 19

Which of the following are appropriate for integration by substitution? (Check all that apply.)

Accepted Answer

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

Question 20

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the consumer surplus.

Accepted Answer

A) $1125 
B) $625 
C) $825 
D) $1300 
A) $1125 
B) $625 
C) $825 
D) $1300

Compute .

The following graph represents the rate of change of a function f with respect to x; i.e., it is the graph of , with . Find a value a to one decimal place such that and . If there is no such value, enter "none".

A family invests in a snow cone stand that has an annual income of $10,000. If they plan to keep the stand for 10 years and save all of the income in an account earning 4.5% interest, compounded continuously, what will their total savings be?

Supply and demand curves for a product are shown in the following figure. Suppose an artificially low price of $300 is imposed. Estimate the total gains from trade now, to the nearest 500 dollars.

Evaluate .

Find

Find

Find an antiderivative of such that .

Find the indefinite integral .

From the time a child is born until he is 18, a father plans to set aside $100 times the child's current age each year. Find the present value of this income stream, given an interest rate of 7% compounded continuously. Round to the nearest dollar.

Consider . What is the definite integral obtained after making the substitution ?

Given the following graph of and the fact that , determine whether is positive or negative.

Evaluate .

Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

Find using integration by substitution.

Evaluate .

Which of the following are appropriate for integration by substitution? (Check all that apply.)

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the consumer surplus.

Functions and Change

Rate of Change: the Derivative

Shortcuts to Differentiation

Using the Derivative

Accumulated Change: the Definite Integral

Probability

Functions of Several Variables

Mathematical Modeling Using Differential Equations

Geometric Series

Filters

Exam 6: Antiderivatives and Applications

Compute .

The following graph represents the rate of change of a function f with respect to x; i.e., it is the graph of , with . Find a value a to one decimal place such that and . If there is no such value, enter "none".

A family invests in a snow cone stand that has an annual income of $10,000. If they plan to keep the stand for 10 years and save all of the income in an account earning 4.5% interest, compounded continuously, what will their total savings be?

Supply and demand curves for a product are shown in the following figure. Suppose an artificially low price of $300 is imposed. Estimate the total gains from trade now, to the nearest 500 dollars.

Evaluate .

Find

Find

Find an antiderivative of such that .

Find the indefinite integral .

From the time a child is born until he is 18, a father plans to set aside $100 times the child's current age each year. Find the present value of this income stream, given an interest rate of 7% compounded continuously. Round to the nearest dollar.

Consider . What is the definite integral obtained after making the substitution ?

Given the following graph of and the fact that , determine whether is positive or negative.

Evaluate .

Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

Find using integration by substitution.

Evaluate .

Which of the following are appropriate for integration by substitution? (Check all that apply.)

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the consumer surplus.

Functions and Change

Rate of Change: the Derivative

Shortcuts to Differentiation

Using the Derivative

Accumulated Change: the Definite Integral

Probability

Functions of Several Variables

Mathematical Modeling Using Differential Equations

Geometric Series

Filters