Question 1

Complete the table by computing  at the given values of x.Use these results to estimate  (if it exists).

Accepted Answer

A) x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 53.91 55.7901 55.979001 56.007001 56.0701 56.71
 
B) x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 54.61 55.8601 55.986001 56.014001 56.1401 57.41
 
C) x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 54.41 55.8401 55.984001 56.012001 56.1201 57.21
 
D) x 6.9 6.99 6.999 7.001 7.01 7.1 f(x) 55.01 55.9001 55.990001 56.018001 56.1801 57.81
The limit does not exist

Question 2

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

Accepted Answer

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

Question 3

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 4

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.
f(x) = -10  = __________

Accepted Answer

The answer of Use the four-step process to find the...

Question 5

Use the graph of the function f to find  and  if the limit exists.

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Find functions f and g such that  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

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 8

Productivity and yield of cultivated crops are often reduced by insect pests.The following graph shows the relationship between the yield of a certain crop,  , as a function of the density of aphids x.(Aphids are small insects that suck plant juices.) Here,  is measured in kilograms/ 4,000 square meters, and x is measured in hundreds of aphids/bean stem.By computing the slopes of the respective tangent lines, estimate the rate of change of the crop yield with respect to the density of aphids when that density is 200 aphids/bean stem and when it is 800 aphids/bean stem.

Accepted Answer

The answer of Productivity and yield of cultivated crops are...

Question 9

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Suppliers of transistor radios will market 10,000 units when the unit price is $55 and 62,500 units when the unit price is $100.Determine the supply function if it is known to have the form  where x is the quantity supplied and p is the unit price in dollars.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

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 12

Determine whether the equation defines y as a linear function of x.

Accepted Answer

A) No, the equation does not define y as a linear function of x 
B) Yes, the equation defines y as a linear function of x

Question 13

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.  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 14

Determine all values of x at which the function is discontinuous.   __________

Accepted Answer

The answer of Determine all values of x at which...

Question 15

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.
Equilibrium quantity: __________ thousand units
Equilibrium price: $ __________

Accepted Answer

The answer of For the pair of supply and demand...

Question 16

The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $800/person/day if exactly 20 people sign up for the cruise.However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $4 for each additional passenger.Assume at least 20 people sign up for the cruise and let x denote the number of passengers above 20.Find a function R giving the revenue/day realized from the charter.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 18

Determine all values of x at which the function is discontinuous.

Accepted Answer

A)   
B)   
C)   
D)

Question 19

A study of driving costs of 1992 model subcompact (four-cylinder) cars found that the average cost (car payments, gas, insurance, upkeep, and depreciation), measured in cents/mile, is approximated by the function  where x denotes the number of miles (in thousands) the car is driven in a year.What happens to the average cost as the number of miles driven increases without bound? Express your answer to the nearest tenth, if necessary.
It approaches __________  .

Accepted Answer

The answer of A study of driving costs of 1992...

Question 20

Let  . Find the zeros of f in  by solving the equation  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 2: Functions, Limits and the Derivative

Complete the table by computing at the given values of x.Use these results to estimate (if it exists) .

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

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

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. f(x) = -10 = __________

Use the graph of the function f to find and if the limit exists.

Find functions f and g such that .

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

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Suppliers of transistor radios will market 10,000 units when the unit price is $55 and 62,500 units when the unit price is $100.Determine the supply function if it is known to have the form where x is the quantity supplied and p is the unit price in dollars.

Determine whether the equation defines y as a linear function of x.

Determine all values of x at which the function is discontinuous. __________

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. Equilibrium quantity: thousand units Equilibrium price: $

Find function f such that and

Determine all values of x at which the function is discontinuous.

Let . Find the zeros of f in by solving the equation .

Exam 2: Functions, Limits and the Derivative

Complete the table by computing at the given values of x.Use these results to estimate (if it exists) .

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

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

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. f(x) = -10 = __________

Use the graph of the function f to find and if the limit exists.

Find functions f and g such that .

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

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Suppliers of transistor radios will market 10,000 units when the unit price is $55 and 62,500 units when the unit price is $100.Determine the supply function if it is known to have the form where x is the quantity supplied and p is the unit price in dollars.

Determine whether the equation defines y as a linear function of x.

Determine all values of x at which the function is discontinuous. __________

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. Equilibrium quantity: __________ thousand units Equilibrium price: $ __________

Find function f such that and

Determine all values of x at which the function is discontinuous.

Let . Find the zeros of f in by solving the equation .

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

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

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. Equilibrium quantity: thousand units Equilibrium price: $