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2.4 Continuity and One-Sided Limits
97
____ 15. Find the constant a such that the function
is continuous on the entire real line.
1
____ 16. Find the constant a such that the function
is continuous on the entire real line.
a.
b.
c.
d.
e.
____ 17. Find the value of c guaranteed by the Intermediate Value Theorem.
a.
b.
c.
d.
e.
98 Chapter 2: Limits and Their Properties
____ 18. Find the value of c guaranteed by the Intermediate Value Theorem.
a.
b.
c.
d.
e.
____ 19. A long distance phone service charges $ for the first minutes and $ for each
additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call
in terms of time t (in minutes).
a.
b.
c.
d.
e.
2.4 Continuity and One-Sided Limits
99
____ 20. Find all values of c such that is continuous on .
a.
b.
c.
d.
e.
100 Chapter 2: Limits and Their Properties
2.4 Continuity and One-Sided Limits
Answer Section
2.5 Infinite Limits
101
2.5 Infinite Limits
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine whether approaches or as x approaches from
the left and from the right by completing the tables below.
–3.1
–3.01
–3.001
–2.999
–2.99
–2.9
–2.5
a.
b.
c.
d.
____ 2. Find all the vertical asymptotes (if any) of the graph of the function
no vertical asymptotes
____ 3. Find the vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
102 Chapter 2: Limits and Their Properties
____ 4. Find all the vertical asymptotes (if any) of the graph of the function
.
a.
b.
c.
d.
e.
____ 5. Find all the vertical asymptotes (if any) of the graph of the function .
a.
b.
c.
d.
e.
____ 6. Find all vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
____ 7. Find the vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
2.5 Infinite Limits
103
____ 8. Find the limit.
a.
b.
c.
d.
e.
____ 9. Find the limit.
a.
b.
c.
d.
e.
____ 10. Find the limit.
a.
b.
c.
d.
e.
____ 11. Find the following limit if it exists: . Use when appropriate.
a.
b.
c.
d.
e.
104 Chapter 2: Limits and Their Properties
____ 12. Find the limit (if it exists).
a.
b.
c.
d.
e.
____ 13. Use a graphing utility to graph the function and determine the
one-sided limit .
0
8
____ 14. Use a graphing utility to graph the function and determine the
following one-sided limit.
a.
b.
c.
d.
e.
2.5 Infinite Limits
105
____ 15.
A petrol car is parked
feet from a long warehouse (see figure). The revolving
light on top of the car turns at a rate of
revolution per second. The rate at which the light beam
moves along the wall is
. Find the rate when is .
a.
b.
c.
d.
e.
106
Chapter 2: Limits and Their Properties
____
16.
A petrol car is parked
feet from a long warehouse (see figure). The revolving
light on top of the car turns at a rate of
revolution per second. The rate at which the light beam
moves along the wall is
. Find the limit of r as
.
65
____ 17. A -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled
away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of
, where x is the distance between the base of the ladder and the house. Find the
rate r when x is feet.
2.5 Infinite Limits
107
32 ft/sec
43 ft/sec
23 ft/sec
34 ft/sec
____ 18. A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled
away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of
where x is the distance between the base of the ladder and the house. Find the
limit of r as .
a.
b.
c.
d.
e.
108 Chapter 2: Limits and Their Properties
2.5 Infinite Limits
Answer Section
