Question 1

During the construction of a high-rise building, a worker accidentally dropped his portable electric screwdriver from a height of 400 ft. After t sec, the screwdriver had fallen a distance of  ft.
How long did it take the screwdriver to reach the ground?
__________ sec
What was the average velocity of the screwdriver between the time it was dropped and the time it hit the ground?
__________ ft/sec
What was the velocity of the screwdriver at the time it hit the ground?
__________ ft/sec

Accepted Answer

The answer of During the construction of a high-rise building,...

Question 2

Let  . Find the rule for the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Find the indicated limit.

Accepted Answer

The answer of Find the indicated limit. ...

Question 4

An apple orchard has an average yield of 35 bushels of apples/tree if tree density is 25 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. Letting x denote the number of trees beyond 25/acre, find a function in x that gives the yield of apples.

Accepted Answer

The answer of An apple orchard has an average yield...

Question 5

Find the one-sided limit, if it exists.

Accepted Answer

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

Question 6

Find the indicated limit, if it exists.

Accepted Answer

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

Question 7

Complete the table by computing  at the given values of x. Use the results to guess at  if it exists.

Accepted Answer

A)  x 1 5 10 100 1,000 f(x) 18 614 4,989 4,990,089 4,999,000,089
 
B)  x 1 5 10 100 1,000 f(x) 18 614 4,439 4,989,539 4,998,999,539
 
C)  x 1 5 10 100 1,000 f(x) 18 614 5,896 4,990,996 4,999,000,996
 
D)  x 1 5 10 100 1,000 f(x) 18 614 4,914 4,990,014 4,999,000,014

Question 8

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)

Question 9

Find the limit, if it exists.

Accepted Answer

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

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 4 units of the commodity available in the market.

Accepted Answer

A)  p = $73 
B)  p = $69 
C)  p = $128 
D)  p = $133 
E)  p = $85

Question 11

Determine the domain of the given equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Let f be the function defined by  Find    and   = __________  = __________  = __________  = __________

Accepted Answer

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

Question 14

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: $150 million; after the 2nd month: $103.8 million; after the 3rd month: $75 million; in the long run: $30 million. 
B)  After the 1st month: $37.5 million; after the 2nd month: $103.8 million; after the 3rd month: $75 million; in the long run: $30 million. 
C)  After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.8 million; in the long run: $150 million. 
D)  After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.8 million; in the long run: $37.5 million. 
E)  After the 1st month: $30 million; after the 2nd month: $75 million; after the 3rd month: $103.7 million; in the long run: $150 million.

Question 15

Ace Truck leases its 10-ft box truck at $25/day and $0.45/mi, whereas Acme Truck leases a similar truck at $20/day and $0.55/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

Accepted Answer

A)  20 + 25x, 0.55 + 0.45x 
B)  25 + 20x, 0.45 + 0.55x 
C)  25 + 0.55x, 20 + 0.45x 
D)  25 + 0.45x, 20 + 0.55x 
E)  0.45 + 25x, 0.55 + 20x

Question 16

Let  Find the derivative  of  .  __________
Find the equation of the tangent line to the curve at the point  .
__________
Select the correct graph of  by answering A, B, or 
C.
__________

Accepted Answer

The answer of Let  Find the derivative  of...

Question 17

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

Accepted Answer

A)  m = 1 and b = 1 
B)  m = 8 and b = -4 
C)  m = -4 and b = 8 
D)  m = 1 and b = 8 
E)  m = 1 and b = -4

Question 18

For the demand equation  where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, select the demand curve.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Find function f such that   and

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 2: Functions, Limits and the Derivative

Let . Find the rule for the function .

Find the indicated limit.

An apple orchard has an average yield of 35 bushels of apples/tree if tree density is 25 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. Letting x denote the number of trees beyond 25/acre, find a function in x that gives the yield of apples.

Find the one-sided limit, if it exists.

Find the indicated limit, if it exists.

Complete the table by computing at the given values of x. Use the results to guess at if it exists.

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 limit, if it exists.

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 4 units of the commodity available in the market.

Determine the domain of the given equation.

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

Let f be the function defined by Find and = = = =

Ace Truck leases its 10-ft box truck at $25/day and $0.45/mi, whereas Acme Truck leases a similar truck at $20/day and $0.55/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

Let Find the derivative of . Find the equation of the tangent line to the curve at the point . Select the correct graph of by answering A, B, or C. __

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, select the demand curve.

Find the limit.

Find function f such that and

Exam 2: Functions, Limits and the Derivative

Let . Find the rule for the function .

Find the indicated limit.

An apple orchard has an average yield of 35 bushels of apples/tree if tree density is 25 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. Letting x denote the number of trees beyond 25/acre, find a function in x that gives the yield of apples.

Find the one-sided limit, if it exists.

Find the indicated limit, if it exists.

Complete the table by computing at the given values of x. Use the results to guess at if it exists.

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 limit, if it exists.

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 4 units of the commodity available in the market.

Determine the domain of the given equation.

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

Let f be the function defined by Find and = __________ = __________ = __________ = __________

Ace Truck leases its 10-ft box truck at $25/day and $0.45/mi, whereas Acme Truck leases a similar truck at $20/day and $0.55/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

Let Find the derivative of . __________ Find the equation of the tangent line to the curve at the point . __________ Select the correct graph of by answering A, B, or C. __________

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, select the demand curve.

Find the limit.

Find function f such that and

Let f be the function defined by Find and = = = =

Let Find the derivative of . Find the equation of the tangent line to the curve at the point . Select the correct graph of by answering A, B, or C. __