Deck 11: Limits and Continuity

Question 1

Find:
f(x)

Answer 1

3

Question 2

Find:

Answer 2

3

Question 3

Find: lim
x→3

Answer 3

6

Question 4

Find: $\lim_{x \rightarrow 5}$ $\frac{x^{2}}{h}$

Question 5

Find:

Question 6

Find:
f(x)

Question 7

Find:

Question 8

Find: lim
p→e

Question 9

Find: lim 15
x→8

Question 10

Find:

Question 11

Find:

Question 12

Find:

Question 13

Find:

Question 14

Find:
f(x)

Question 15

Find:

Question 16

Find:

Question 17

Find:
f(x)

Question 18

Find: lim (
- 4x + 3)
x→3

Question 19

Find:

Question 20

Find:

Question 21

=

A) 0
B) 2
C) -4
D) 4
E) -∞

Question 22

Find:
81

Question 23

(2 +
)=

A) 0
B)
C) -2 +
D) 2 +
E) does not exist

Question 24

If f(x)= 2x + 7,find

by treating x as a constant.

Question 25

Find:

Question 26

=

A) 0
B) -
C)
D) -∞
E) ∞

Question 27

If f(x)= 3x - 4,find

by treating x as a constant.

Question 28

=

A) 0
B)
C)
D)
E)

Question 29

=

A)
B)
C) -1
D) -∞
E) ∞

Question 30

Find

where f(x)=

Question 31

Find

where f(x)=
+ 3x + 5

Question 32

=

A)
B) 2
C) 3
D) 4
E) 5

Question 33

Find: Find

Question 34

Find

where f(x)=

Question 35

If f(x)= 6,find

by treating x as a constant.

Question 36

Find: Find

Question 37

=

A) 0
B) x
C) -∞
D) ∞
E) does not exist

Question 38

If f(x)= 3x - 7,then
=

A) 0.
B) 3.
C) 3x.
D) -7.
E) does not exist

Question 39

Find: Find

Question 40

=

A) 0
B) 1
C) -4
D) -
E) ∞

Question 41

The revenue function for a certain product is given by R(x)= 500x -
.Find
R(x).

Question 42

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)=
π
.Graph V(r)in the standard viewing rectangle,
×
and use TRACE to estimate
V(r).

Question 43

The revenue function for a certain product is given by R(x)= 500x -
.Graph this function in the window
×
.Use TRACE to estimate
R(x).

Question 44

If the profit function for a certain business is given by: P(x)= 225x -
- 800,use the rule about the limit of a polynomial function to determine
P(x).

Question 45

The revenue function for a certain product is given by R(x)= 500x -
.Find
R(x).

Question 46

If the profit function for a certain business is given by: P(x)= 225x -
- 800,use the rule about the limit of a polynomial function to determine
P(x).

Question 47

The revenue function for a certain product is given by R(x)= 500x -
.Find
R(x).

Question 48

The greatest integer function in mathematics (denoted f(x)=
)is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus
= 1).By considering
,
,
,
,and
,determine

.

Question 49

The greatest integer function in mathematics (denoted f(x)=
)is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus
= 1).By considering
,
,
,
,and
,determine

.

Question 50

If the profit function for a certain business is given by: P(x)= 225x -
- 800,use the rule about the limit of a polynomial function to determine
P(x).

Question 51

The revenue function for a certain product is given by R(x)= 500x -
.Graph this function in the window
×
.Use TRACE to estimate
R(x).

Question 52

If the profit function for a certain business is given by: P(x)= 225x -
- 800,use the rule about the limit of a polynomial function to determine
P(x).

Question 53

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)=
π
.Find
V(r).

Question 54

Find: Find

Question 55

Find: Find

Question 56

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)=
π
.Graph V(r)in the standard viewing rectangle,
×
and use TRACE to estimate
V(r).

Question 57

The greatest integer function in mathematics (denoted f(x)=
)is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus
= 1).By considering
,
,
,
,and
,determine

.

Question 58

The greatest integer function in mathematics (denoted f(x)=
)is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus
= 1).By considering
,
,
,
,and
,determine

.

Question 59

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)=
π
.Find
V(r).

Question 60

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)=
π
.Find
V(r).

Question 61

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 62

Find:
g(x)

Question 63

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 64

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 65

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 66

The length of a material increases as it is heated up according to the equation
The rate at which the length is increasing is given by:
Calculate this limit.

Question 67

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 68

The profit function for a certain business is given by: P(x)= 225x -
- 800.Graph this function on your graphing calculator and use the evaluation function to determine
P(x)using the rule about the limit of a polynomial function.

Question 69

Use your calculator to complete the table,and use your results to estimate the given limit.

Question 70

The rate of change of productivity p (in number of units produced per hour)increases with time on the job by the function p =
.Find
p.

Question 71

Find:


.If the limit does not exist,so state or use the symbol ∞ or
if appropriate.

Question 72

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 73

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 74

The rate of change of productivity p (in number of units produced per hour)increases with time on the job by the function p =
.Find
p.

Question 75

The rate of change of productivity p (in number of units produced per hour)increases with time on the job by the function p =
.Find
p.

Question 76

Find:
f(x)

Question 77

The length of a material increases as it is heated up according to the equation
The rate at which the length is increasing is given by:
Calculate this limit.

Question 78

Use your calculator to complete the table,and use your results to estimate the given limit.

Question 79

Find:

.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Question 80

The length of a material increases as it is heated up according to the equation
The rate at which the length is increasing is given by:
Calculate this limit.