Question 1

Find the second derivative of the function.

Accepted Answer

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

Question 2

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The function   is continuous on   .

Accepted Answer

A)  The function   is continuous but zero when
  , then the function
  is not continuous in
  , so the statement is false. 
B)  The function   is continuous and nonzero on
  , then the function
  is continuous in
  , so the statement is true. 
A)  The function   is continuous but zero when
  , then the function
  is not continuous in
  , so the statement is false. 
B)  The function   is continuous and nonzero on
  , then the function
  is continuous in
  , so the statement is true.

Question 3

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 4

Find the second derivative of the function.

Accepted Answer

The answer of Find the second derivative of the function....

Question 5

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by   . How fast is the price of the commodity changing at   ?

Accepted Answer

A)  Increasing at the rate of $19/wk. 
B)  Decreasing at the rate of $19/wk. 
C)  Increasing at the rate of $14/wk. 
D)  Decreasing at the rate of $14/wk. 
E)  Increasing at the rate of $5/wk. 
A)  Increasing at the rate of $19/wk. 
B)  Decreasing at the rate of $19/wk. 
C)  Increasing at the rate of $14/wk. 
D)  Decreasing at the rate of $14/wk. 
E)  Increasing at the rate of $5/wk.

Question 6

The radioactive element polonium decays according to the law   where   is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?

Accepted Answer

A)  The initial amount was 642 mg 
B)  The initial amount was 640 mg 
C)  The initial amount was 635 mg 
D)  The initial amount was 629 mg 
A)  The initial amount was 642 mg 
B)  The initial amount was 640 mg 
C)  The initial amount was 635 mg 
D)  The initial amount was 629 mg

Question 7

Find the derivative of the function.

Accepted Answer

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

Question 8

Find the second derivative of the function.

Accepted Answer

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

Question 9

The Ehrenberg equation   gives the relationship between the height (in meters) and the average weight W (in kilograms) for children between 5 and 13 years of age. What is the average weight of a 10-year-old child who stands at 1.44 m tall? Round the answer to the nearest tenth. Use differentials to estimate the change in the average weight of a 10-year-old child whose height increases from 1.44 m to 1.49 m.

Accepted Answer

A)  48.3 kg, 3.4 kg 
B)  34.0 kg, 3.1 kg 
C)  62.5 kg, 1.7 kg 
D)  83.9 kg, 3.1 kg 
E)  34.0 kg, 1.7 kg 
A)  48.3 kg, 3.4 kg 
B)  34.0 kg, 3.1 kg 
C)  62.5 kg, 1.7 kg 
D)  83.9 kg, 3.1 kg 
E)  34.0 kg, 1.7 kg

Question 10

How long will it take $5,000 to grow to $6,500 if the investment earns interest at the rate of 13% / year compounded monthly?

Accepted Answer

A)  1.9 year(s) 
B)  1.7 year(s) 
C)  1.6 year(s) 
D)  2.0 year(s) 
A)  1.9 year(s) 
B)  1.7 year(s) 
C)  1.6 year(s) 
D)  2.0 year(s)

Question 11

The unit selling price p (in dollars) and the quantity demanded (in pairs) of a certain brand of women's gloves is given by the demand equation   . What is the marginal revenue to the nearest cent per day when x = 10?

Accepted Answer

A)  The marginal revenue when x = 10 is $160 per day. 
B)  The marginal revenue when x = 10 is $147.41 per day. 
C)  The marginal revenue when x = 10 is $0.99 per day. 
D)  The marginal revenue when x = 10 is $158.41 per day. 
A)  The marginal revenue when x = 10 is $160 per day. 
B)  The marginal revenue when x = 10 is $147.41 per day. 
C)  The marginal revenue when x = 10 is $0.99 per day. 
D)  The marginal revenue when x = 10 is $158.41 per day.

Question 12

Find the second derivative of the function.

Accepted Answer

The answer of Find the second derivative of the function....

Question 13

Express the equation in logarithmic form.

Accepted Answer

The answer of Express the equation in logarithmic form. ...

Question 14

The monthly demand for a certain brand of perfume is given by the demand equation   where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.

Accepted Answer

A)  The rate of change of the price is - 3.62 cents per bottle. 
B)  The rate of change of the price is 5.24 cents per bottle. 
C)  The rate of change of the price is - 2.62 cents per bottle. 
D)  The rate of change of the price is - 2.22 cents per bottle. 
A)  The rate of change of the price is - 3.62 cents per bottle. 
B)  The rate of change of the price is 5.24 cents per bottle. 
C)  The rate of change of the price is - 2.62 cents per bottle. 
D)  The rate of change of the price is - 2.22 cents per bottle.

Question 15

Express the equation in logarithmic form.

Accepted Answer

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

Question 16

Sketch the graph of the equation.

Accepted Answer

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

Question 17

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 18

Use the laws of logarithms to simplify the expression.

Accepted Answer

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

Question 19

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 20

According to data obtained from the CBO, the total federal debt (in trillions of dollars) from 2001 through 2006 is given by     where t is measured in years, with   corresponding to 2001. How fast was the total federal debt increasing in 2002? round answer to three decimal places.

Accepted Answer

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

Find the second derivative of the function.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The function is continuous on .

Find the derivative of the function.

Find the second derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . How fast is the price of the commodity changing at ?

The radioactive element polonium decays according to the law where is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?

Find the derivative of the function.

Find the second derivative of the function.

How long will it take $5,000 to grow to $6,500 if the investment earns interest at the rate of 13% / year compounded monthly?

The unit selling price p (in dollars) and the quantity demanded (in pairs) of a certain brand of women's gloves is given by the demand equation . What is the marginal revenue to the nearest cent per day when x = 10?

Find the second derivative of the function.

Express the equation in logarithmic form.

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.

Express the equation in logarithmic form.

Sketch the graph of the equation.

Find the derivative of the function.

Use the laws of logarithms to simplify the expression.

Find the derivative of the function.

According to data obtained from the CBO, the total federal debt (in trillions of dollars) from 2001 through 2006 is given by where t is measured in years, with corresponding to 2001. How fast was the total federal debt increasing in 2002? round answer to three decimal places.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 5: Exponential and Logarithmic Functions

Find the second derivative of the function.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The function is continuous on .

Find the derivative of the function.

Find the second derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . How fast is the price of the commodity changing at ?

The radioactive element polonium decays according to the law where is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?

Find the derivative of the function.

Find the second derivative of the function.

How long will it take $5,000 to grow to $6,500 if the investment earns interest at the rate of 13% / year compounded monthly?

The unit selling price p (in dollars) and the quantity demanded (in pairs) of a certain brand of women's gloves is given by the demand equation . What is the marginal revenue to the nearest cent per day when x = 10?

Find the second derivative of the function.

Express the equation in logarithmic form.

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.

Express the equation in logarithmic form.

Sketch the graph of the equation.

Find the derivative of the function.

Use the laws of logarithms to simplify the expression.

Find the derivative of the function.

According to data obtained from the CBO, the total federal debt (in trillions of dollars) from 2001 through 2006 is given by where t is measured in years, with corresponding to 2001. How fast was the total federal debt increasing in 2002? round answer to three decimal places.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters