Question 1

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

Accepted Answer

A)   
B)   
C)   
D)

Question 2

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 3

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $51/unit.
What is the cost function?
__________
What is the revenue function?
__________
What is the profit function?
__________

Accepted Answer

The answer of A manufacturer has a monthly fixed cost...

Question 4

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

Accepted Answer

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

Question 5

Let f be the function defined by
  Find f (0), f (4), and f (8).  __________  __________  __________

Accepted Answer

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

Question 6

Find the one-sided limit, if it exists.

Accepted Answer

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

Question 7

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

Accepted Answer

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

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

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

Accepted Answer

The answer of If f and g are functions, then...

Question 10

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 6-in. radius?

Accepted Answer

The answer of The circumference of a circle is given...

Question 11

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?

Accepted Answer

A)  It approaches 15.39  . 
B)  It approaches 2,290  . 
C)  It increases without bound. 
D)  It becomes infinitely small.

Question 12

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.  __________ units  $ __________

Accepted Answer

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

Question 13

Let  and  . Find the rule for the function  .

Accepted Answer

The answer of Let  and  . Find the...

Question 14

Find the limit.

Accepted Answer

The answer of Find the limit. ...

Question 15

Find the constants m in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2.
__________
Find the constants b in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2.
__________

Accepted Answer

The answer of Find the constants m in the linear...

Question 16

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. Select a graph showing his earnings as a function of the level of his sales x.    Select the correct graph. Answer A, B, or 
C. __________
Determine the values of x for which the function f is discontinuous. Give the least three values of x.
  __________

Accepted Answer

The answer of The base salary of a salesman working...

Question 17

The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by  with t = 0 corresponding to the beginning of 1995.
Round the answers to two decimal places, if necessary.
What will be the ratio at the beginning of 2005?
__________
At the beginning of 2020?
__________

Accepted Answer

The answer of The ratio of working-age population to the...

Question 18

The oxygen consumption (in milliliter/pound/minute) for a person walking at x mph is approximated by the function  where the oxygen consumption for a runner at x mph is approximated by the function  At what speed is the oxygen consumption the same for a walker as it is for a runner? What is the level of oxygen consumption at that speed?

Accepted Answer

A)  3.1 mph, 99.6 mL/lb/min 
B)  7.1 mph, 89.6 mL/lb/min 
C)  7.6 mph, 94.6 mL/lb/min 
D)  4.6 mph, 64.6 mL/lb/min 
E)  5.6 mph, 74.6 mL/lb/min

Question 19

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

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

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

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.

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $51/unit. What is the cost function? What is the revenue function? What is the profit function? __

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

Let f be the function defined by Find f (0), f (4), and f (8). __

Find the one-sided limit, if it exists.

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

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

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

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 6-in. radius?

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. units $

Let and . Find the rule for the function .

Find the limit.

Find the constants m in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2. Find the constants b in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2.

The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by with t = 0 corresponding to the beginning of 1995. Round the answers to two decimal places, if necessary. What will be the ratio at the beginning of 2005? At the beginning of 2020?

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

Find function f such that and

Exam 2: Functions, Limits and the Derivative

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.

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.

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $51/unit. What is the cost function? __________ What is the revenue function? __________ What is the profit function? __________

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

Let f be the function defined by Find f (0), f (4), and f (8). __________ __________ __________

Find the one-sided limit, if it exists.

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

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

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

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 6-in. radius?

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. __________ units $ __________

Let and . Find the rule for the function .

Find the limit.

Find the constants m in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2. __________ Find the constants b in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2. __________

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

Find function f such that and

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $51/unit. What is the cost function? What is the revenue function? What is the profit function? __

Let f be the function defined by Find f (0), f (4), and f (8). __

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

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. units $

Find the constants m in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2. Find the constants b in the linear function f (x) = mx + b, so that f (0) = 6 and f (2) = -2.