Question 1

Let   ,   .Find the rule for the function   .

Accepted Answer

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

Question 2

The number of IBM shares that Nancy owns is given by f (t).The price per share of the stock of IBM at time t is g(t) dollars.What does the function f (t)g(t) represent?

Accepted Answer

A) The value in dollars of Nancy's shares of IBM at time t 
B) The total number of IBM shares at time t 
C) The number of IBM shares that Nancy owns at time t 
D) The price per share of the stock of IBM at time t 
A) The value in dollars of Nancy's shares of IBM at time t 
B) The total number of IBM shares at time t 
C) The number of IBM shares that Nancy owns at time t 
D) The price per share of the stock of IBM at time t

Question 3

Economists define the disposable annual income for an individual by the equation D = (1 - r)T, where T is the individual's total income and r is the net rate at which he or she is taxed.What is the disposable income for an individual whose income is $90,000 and whose net tax rate is 35%?

Accepted Answer

A) $31,500 
B) $58,500 
C) $148,500 
D) $90,000 
E) $207,000 
A) $31,500 
B) $58,500 
C) $148,500 
D) $90,000 
E) $207,000

Question 4

For the pair of supply and demand equations   where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Accepted Answer

A) x = 11.5, p = $96.50 
B) x = 18.5, p = $233.50 
C) x = 15, p = $135.00 
D) x = 3.5, p = $68.50 
E) x = 18.5, p = $173.50 
A) x = 11.5, p = $96.50 
B) x = 18.5, p = $233.50 
C) x = 15, p = $135.00 
D) x = 3.5, p = $68.50 
E) x = 18.5, p = $173.50

Question 5

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

Accepted Answer

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

Question 6

The graph shows the volume of wood produced in a single-species forest.Here   is measured in cubic meters/hectare and t is measured in years.By computing the slopes of the respective tangent lines, estimate the rate at which the wood grown is changing at the beginning of year 10 and at the beginning of year 40.

Accepted Answer

The answer of The graph shows the volume of wood...

Question 7

Find the indicated limit, if it exists.Otherwise, answer no solution.

Accepted Answer

The answer of Find the indicated limit, if it exists.Otherwise,...

Question 8

The circumference of a circle is given by   where r is the radius of the circle.What is the circumference of a circle with a 5-in.radius?

Accepted Answer

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

Question 9

If f and g are functions, then   .Answer true or false.

Accepted Answer

A) True 
 B)False

Question 10

Determine whether the point (- 6, - 12) lies on the graph of the function.Answer yes or no.

Accepted Answer

The answer of Determine whether the point (- 6, -...

Question 11

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by   where x denotes the number of units manufactured each month.What is Apollo's revenue when 1,500 units are produced?

Accepted Answer

A) $-75,000 
B) $-76,500 
C) $-73,500 
D) $1,500 
E) $-72,000 
A) $-75,000 
B) $-76,500 
C) $-73,500 
D) $1,500 
E) $-72,000

Question 12

Let f be the function defined by f (x) = 8x + 9.Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

Accepted Answer

The answer of Let f be the function defined by...

Question 13

The number of IBM shares that Nancy owns is given by f (t).The price per share of the stock of IBM at time t is g(t) dollars.What does the function f (t)g(t) represent?

Accepted Answer

The value in dollars

Question 14

Find the functions f + g, f - g, fg, and

Accepted Answer

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

Question 15

If f is a function, then f (a + b) = f (a) + f (b).Answer true or false.

Accepted Answer

A) True 
 B)False

Question 16

A function f is continuous at the point   if the following conditions are satisfied.
1.   is defined.
2.   exists.
3.   .
Determine the value of x, if any, at which the function is discontinuous.       __________
State the condition(s) for continuity that are violated.
Conditions: __________

Accepted Answer

The answer of A function f is continuous at the...

Question 17

Find   for the function.Simplify your answer.

Accepted Answer

The answer of Find   for the function.Simplify your...

Question 18

Find the limit.

Accepted Answer

The answer of Find the limit.  ...

Question 19

Determine whether the given function is a polynomial function or rational function.State the degree, if it is polynomial function.   Answer polynomial or rational.__________
If a polynomial function, the degree is __________

Accepted Answer

The answer of Determine whether the given function is a...

Question 20

Find the values of x for which the function is continuous.

Accepted Answer

The answer of Find the values of x for which...

Let , .Find the rule for the function .

The number of IBM shares that Nancy owns is given by f (t).The price per share of the stock of IBM at time t is g(t) dollars.What does the function f (t)g(t) represent?

Economists define the disposable annual income for an individual by the equation D = (1 - r)T, where T is the individual's total income and r is the net rate at which he or she is taxed.What is the disposable income for an individual whose income is $90,000 and whose net tax rate is 35%?

For the pair of supply and demand equations where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

Find the indicated limit, if it exists.Otherwise, answer no solution.

The circumference of a circle is given by where r is the radius of the circle.What is the circumference of a circle with a 5-in.radius?

If f and g are functions, then .Answer true or false.

Determine whether the point (- 6, - 12) lies on the graph of the function.Answer yes or no.

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by where x denotes the number of units manufactured each month.What is Apollo's revenue when 1,500 units are produced?

Let f be the function defined by f (x) = 8x + 9.Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

The number of IBM shares that Nancy owns is given by f (t).The price per share of the stock of IBM at time t is g(t) dollars.What does the function f (t)g(t) represent?

Find the functions f + g, f - g, fg, and

If f is a function, then f (a + b) = f (a) + f (b).Answer true or false.

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. State the condition(s) for continuity that are violated. Conditions:

Find for the function.Simplify your answer.

Find the limit.

Determine whether the given function is a polynomial function or rational function.State the degree, if it is polynomial function. Answer polynomial or rational. If a polynomial function, the degree is

Find the values of x for which the function is continuous.

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 2: Functions, Limits and the Derivative

Let , .Find the rule for the function .

The number of IBM shares that Nancy owns is given by f (t).The price per share of the stock of IBM at time t is g(t) dollars.What does the function f (t)g(t) represent?

Economists define the disposable annual income for an individual by the equation D = (1 - r)T, where T is the individual's total income and r is the net rate at which he or she is taxed.What is the disposable income for an individual whose income is $90,000 and whose net tax rate is 35%?

For the pair of supply and demand equations where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

Find the indicated limit, if it exists.Otherwise, answer no solution.

The circumference of a circle is given by where r is the radius of the circle.What is the circumference of a circle with a 5-in.radius?

If f and g are functions, then .Answer true or false.

Determine whether the point (- 6, - 12) lies on the graph of the function.Answer yes or no.

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by where x denotes the number of units manufactured each month.What is Apollo's revenue when 1,500 units are produced?

Let f be the function defined by f (x) = 8x + 9.Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

The number of IBM shares that Nancy owns is given by f (t).The price per share of the stock of IBM at time t is g(t) dollars.What does the function f (t)g(t) represent?

Find the functions f + g, f - g, fg, and

If f is a function, then f (a + b) = f (a) + f (b).Answer true or false.

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. __________ State the condition(s) for continuity that are violated. Conditions: __________

Find for the function.Simplify your answer.

Find the limit.

Determine whether the given function is a polynomial function or rational function.State the degree, if it is polynomial function. Answer polynomial or rational.__________ If a polynomial function, the degree is __________

Find the values of x for which the function is continuous.

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. State the condition(s) for continuity that are violated. Conditions:

Determine whether the given function is a polynomial function or rational function.State the degree, if it is polynomial function. Answer polynomial or rational. If a polynomial function, the degree is