Question 1

Sketch the graph of the function  and evaluate  , if it exists, for the given value of  .

Accepted Answer

A)  
 
B)  
 
C)  
 
D)  
 
E)

Question 2

Let  Find the value of k that will make f continuous on  .

Accepted Answer

A)   
B)   
C)   
D)

Question 3

The base salary of a salesman working on commission is $13,000. For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x.

Accepted Answer

A)   
B)   
C)

Question 4

Evaluate h (2), where    h (2) = __________

Accepted Answer

The answer of Evaluate h (2), where   ...

Question 5

Let  ,  . Find the rule for the function f - g.

Accepted Answer

The answer of Let  ,  . Find the...

Question 6

Find the one-sided limit, if it exists. If it does not, answer none.

Accepted Answer

The answer of Find the one-sided limit, if it exists....

Question 7

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Refer to the graph of the function f and determine whether the statement below is true or false.

Accepted Answer

The answer of Refer to the graph of the function...

Question 9

The position of car A and car B, starting out side by side and traveling along a straight road, is given by  and  , respectively, where s is measured in feet and t is measured in seconds (see the accompanying figure).  Which car is traveling faster at  ?
Car __________
Which car is traveling faster at  ?
Hint: Compare tangent lines.
Car __________
Which car is traveling faster at  ?
Car __________

Accepted Answer

The answer of The position of car A and car...

Question 10

For the supply equation  where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 3 units of the commodity available in the market.

Accepted Answer

A)  p = $57 
B)  p = $89 
C)  p = $47 
D)  p = $95 
E)  p = $9

Question 11

Find the indicated limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Let  Find the equation of the tangent line to the curve at the point  .

Accepted Answer

A)   
B)   
C)   
D)

Question 13

For the demand equation  where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

Accepted Answer

A)  x = 9,000 units 
B)  x = 4,500 units 
C)  x = 90 units 
D)  x = 3,000 units 
E)  x = 900 units

Question 14

For the supply equation  where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 2 units of the commodity available in the market.
$__________

Accepted Answer

The answer of For the supply equation  where x...

Question 15

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

Question 16

Find and simplify  for the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

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 answer of The number of IBM shares that Nancy...

Question 18

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $40/unit. What is the cost function? What is the revenue function? What is the profit function?

Accepted Answer

A)  C(x) = 9x + 45,000, R(x) = 40x and P(x) = 31x - 45,000 
B)  C(x) = 40x + 9, R(x) = 9x and P(x) = -31x + 45,000 
C)  C(x) = 40x + 45,000, R(x) = 45,000x and P(x) = 31x - 45,000 
D)  C(x) = 9x + 45,000, R(x) = 9x and P(x) = 31x + 45,000 
E)  C(x) = 9x + 45,000, R(x) = 45,000x and P(x) = 31x + 45,000

Question 19

Use the graph of the function f to find  and  if the limit exists. If it does not, answer none.   __________  __________  __________

Accepted Answer

The answer of Use the graph of the function f...

Question 20

Find the limit.

Accepted Answer

The answer of Find the limit. ...

Exam 2: Functions, Limits and the Derivative

Sketch the graph of the function and evaluate , if it exists, for the given value of .

Let Find the value of k that will make f continuous on .

The base salary of a salesman working on commission is $13,000. For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission. Sketch a graph showing his earnings as a function of the level of his sales x.

Evaluate h (2), where h (2) = __________

Let , . Find the rule for the function f - g.

Find the one-sided limit, if it exists. If it does not, answer none.

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

Refer to the graph of the function f and determine whether the statement below is true or false.

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 3 units of the commodity available in the market.

Find the indicated limit.

Let Find the equation of the tangent line to the curve at the point .

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 2 units of the commodity available in the market. $__________

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%?

Find and simplify 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?

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $40/unit. What is the cost function? What is the revenue function? What is the profit function?

Use the graph of the function f to find and if the limit exists. If it does not, answer none. __

Find the limit.