Question 1

Find  and  , where

Accepted Answer

A)   
B)   
C)   
D)   
E)  The limits do not exist B

Question 2

Refer to the graph of the function f in the following figure.  Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.

Accepted Answer

A)  f (3)  = 3, f (2)  = 0
B)  f (4)  = 3, f (3)  = 0
C)  f (4)  = 3, f (2)  = 0
D)  f (3)  = 3, f (1)  = 0
E)  f (3)  = 5, f (0)  = -2 A

Question 3

Find the indicated limit.

Accepted Answer

7

Question 4

Use the intermediate value theorem to find the value of c such that  .

Accepted Answer

A)   
B)   
C)   
D)

Question 5

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

Accepted Answer

The answer of Find the values of x for which...

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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

Question 8

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

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 10

Find the limit, if it exists.

Accepted Answer

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

Question 11

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

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

Question 12

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

The function that gives the cost of a certain commodity is defined by  where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars.Sketch the graph of the function

Accepted Answer

A)    
B)    
C)  Determine the values of x for which the function C is discontinuous.
D)

Question 14

Find the indicated one-sided limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Let f be the function defined by  Find f (0), f (25), and f (50).

Accepted Answer

A)  f (0)  = 9, f (25)  = 4, f (50)  = - 1
B)  f (0)  = 29, f (25)  = 4, f (50)  = - 1
C)  f (0)  = 29, f (25)  = 4, f (50)  = - 25
D)  f (0)  = 4, f (25)  =  , f (50)  = - 1
E)  f (0)  = 9, f (25)  =  , f (50)  = - 25

Question 16

Find the indicated limit, if it exists.Otherwise, answer no solution.

Accepted Answer

The answer of Find the indicated limit, if it exists.Otherwise,...

Question 17

The number of homes with digital TVs is expected to grow according to the function  where t is measured in years, with t = 0 corresponding to the beginning of 2000, and f(t) is measured in millions of homes.
Round your answers to the nearest whole number.
How many homes had digital TVs at the beginning of 2000?
__________
How many homes will have digital TVs at the beginning of 2005?
__________

Accepted Answer

The answer of The number of homes with digital TVs...

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  and  , where  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

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

Accepted Answer

The answer of Let  Find the value of k...

Exam 2: Functions, Limits and the Derivative

Find and , where

Refer to the graph of the function f in the following figure. Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.

Find the indicated limit.

Use the intermediate value theorem to find the value of c such that .

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.

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

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

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?

Find the limit, 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. __________

The function that gives the cost of a certain commodity is defined by where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars.Sketch the graph of the function

Find the indicated one-sided limit.

Let f be the function defined by Find f (0) , f (25) , and f (50) .

Find the indicated limit, if it exists.Otherwise, answer no solution.

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 and , where .

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