Question 1

Let  ​ Find the equation of the tangent line to the curve at the point (2, 15).
​

Accepted Answer

A)   
B)  ​  
C)  ​  
D)  ​

Question 2

Find  and  , where
​  ​  = __________
​  = __________

Accepted Answer

The answer of Find  and  , where
​ ...

Question 3

Find the indicated limit, if it exists. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)  The limit does not exist.

Question 4

The total worldwide box-office receipts for a long-running blockbuster movie are approximated by the function  ​ where  is measured in millions of dollars and  is the number of months since the movie's release. What are the total box-office receipts after the first month? The second month? The third month? What will the movie gross in the long run (when  is very large)?
​

Accepted Answer

A)  After the 1st month: $40 million; after the 2nd month: $100 million; after the 3rd month: $138.5 million; in the long run: $200 million. 
B)  After the 1st month: $200 million; after the 2nd month: $138.5 million; after the 3rd month: $100 million; in the long run: $40 million. 
C)  After the 1st month: $40 million; after the 2nd month: $100 million; after the 3rd month: $138.6 million; in the long run: $200 million. 
D)  After the 1st month: $40 million; after the 2nd month: $100 million; after the 3rd month: $138.5 million; in the long run: $50 million. 
E)  After the 1st month: $50 million; after the 2nd month: $138.5 million; after the 3rd month: $100 million; in the long run: $40 million.

Question 5

The management of Titan Tire Company has determined that the weekly demand and supply functions for their Super Titan tires are given by respectively, where p is measured in dollars and x is measured in thousands of units. Find the equilibrium quantity and price. x_b = __________ units p_b = $ __________

Accepted Answer

The answer of The management of Titan Tire Company has...

Question 6

For the supply equations, where x is the quantity supplied in units of a thousand and p is the unit price in dollars, sketch the supply curve. ​  ​

Accepted Answer

A)  ​  
B)  ​  
C)  ​  
D)  ​  
E)  ​

Question 7

Determine whether the statement is true or false.
​
If f is a function, then f (a + b) = f (a) + f (b).
​

Accepted Answer

A) True 
 B)False

Question 8

The total worldwide box-office receipts for a long-running blockbuster movie are approximated by the function  where  is measured in millions of dollars and  is the number of months since the movie's release.
What are the total box-office receipts after the first month? The second month? The third month? Round the answer to the nearest tenth, if necessary.
After the 1st month:
$ __________ million
After the 2nd month:
$ __________ million
After the 3rd month:
$ __________ million
What will the movie gross in the long run (when  is very large)?
$ __________ million

Accepted Answer

The answer of The total worldwide box-office receipts for a...

Question 9

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

Accepted Answer

A)  The given function is a rational function with degree 6 
B)  The given function is a rational function 
C)  The given function is a polynomial function with degree 6 
D)  The given function is a polynomial function with degree 2 
E)  The given function is a polynomial function with degree 12

Question 10

Let  ,  and  . Find the rule for the function  . ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Use the method of bisection to find the root of the equation  , accurate to two decimal places. ​

Accepted Answer

A)   
B)   
C)   
D)

Question 12

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 = 400 units 
B)  x = 3,000 units 
C)  x = 4,000 units 
D)  x = 40 units 
E)  x = 2,000 units

Question 13

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $13,200 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Accepted Answer

The answer of TMI, a manufacturer of blank audiocassette tapes,...

Question 14

Use the graph of the function f to determine  and  .
​  ​
​

Accepted Answer

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

Question 15

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

Accepted Answer

A)   
B)   
C)   
D)

Question 16

Find the limit.
​

Accepted Answer

The answer of Find the limit.
​ ...

Question 17

Find the domain of the function  .

Accepted Answer

The answer of Find the domain of the function ...

Question 18

Find  of the functions. ​  ,  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find the range of the function. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Determine whether the equation defines y as a linear function of x. Answer yes or no.
​

Accepted Answer

The answer of Determine whether the equation defines y as...

Exam 2: Functions, Limits, and the Derivative

Let Find the equation of the tangent line to the curve at the point (2, 15) .

Find and , where = =

Find the indicated limit, if it exists.

For the supply equations, where x is the quantity supplied in units of a thousand and p is the unit price in dollars, sketch the supply curve.

Determine whether the statement is true or false. If f is a function, then f (a + b) = f (a) + f (b).

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

Let , and . Find the rule for the function .

Use the method of bisection to find the root of the equation , accurate to two decimal places.

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.

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $13,200 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Use the graph of the function f to determine and .

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

Find the limit.

Find the domain of the function .

Find of the functions. ,

Find the range of the function.

Determine whether the equation defines y as a linear function of x. Answer yes or no.

Exam 2: Functions, Limits, and the Derivative

Let ​ Find the equation of the tangent line to the curve at the point (2, 15) . ​

Find and , where ​ ​ = __________ ​ = __________

Find the indicated limit, if it exists. ​ ​

For the supply equations, where x is the quantity supplied in units of a thousand and p is the unit price in dollars, sketch the supply curve. ​ ​

Determine whether the statement is true or false. ​ If f is a function, then f (a + b) = f (a) + f (b). ​

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

Let , and . Find the rule for the function . ​

Use the method of bisection to find the root of the equation , accurate to two decimal places. ​

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. ​

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $13,200 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Use the graph of the function f to determine and . ​ ​ ​

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

Find the limit. ​

Find the domain of the function .

Find of the functions. ​ , ​

Find the range of the function. ​ ​

Determine whether the equation defines y as a linear function of x. Answer yes or no. ​

Let Find the equation of the tangent line to the curve at the point (2, 15) .

Find and , where = =

Find the indicated limit, if it exists.

For the supply equations, where x is the quantity supplied in units of a thousand and p is the unit price in dollars, sketch the supply curve.

Determine whether the statement is true or false. If f is a function, then f (a + b) = f (a) + f (b).

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

Let , and . Find the rule for the function .

Use the method of bisection to find the root of the equation , accurate to two decimal places.

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.

Use the graph of the function f to determine and .

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

Find the limit.

Find of the functions. ,

Find the range of the function.

Determine whether the equation defines y as a linear function of x. Answer yes or no.