68 Chapter 1: Limits and Their Properties
1.4 Continuity and One-Sided Limits
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the graph as shown to determine the following limits, and discuss the continuity
of the function at .
(i) (ii) (iii)
a.
b. 2 , 2 , 2 ,
c.
d. 2 , 2 , 2 ,
e.
____ 2. Use the graph as shown to determine the following limits, and discuss the continuity
of the function at .
(i) (ii) (iii)
1.4 Continuity and One-Sided Limits 69
a.
b.
c.
d.
e.
____ 3. Use the graph to determine the following limits, and discuss the continuity of the
function at .
(i) (ii) (iii)
a.
b.
c.
d.
e.
70 Chapter 1: Limits and Their Properties
____ 4. Find the limit (if it exists).
a.
b.
c.
d.
e.
____ 5. Find the limit (if it exists).
a.
b.
c.
d.
e.
____ 6. Find the limit (if it exists).
a.
b.
c.
d.
e.
1.4 Continuity and One-Sided Limits 71
____ 7. Find the limit (if it exists). Note that represents the greatest integer
function.
a.
b.
c.
d.
e.
____ 8. Find the limit (if it exists). Note that represents the greatest integer
function.
a.
b.
c.
d.
e.
____ 9. Discuss the continuity of the function .
a.
b.
c.
d.
e.
72 Chapter 1: Limits and Their Properties
____ 10. Find the x-values (if any) at which the function is not
continuous. Which of the discontinuities are removable?
a.
b.
c.
d.
e.
____ 11. Find the x-values (if any) at which is not continuous.
a.
b.
c.
d.
e.
____ 12. Find the x-values (if any) at which the function is not continuous.
Which of the discontinuities are removable?
a. 10 and – , removable
b. discontinuous everywhere
c. continuous everywhere
d. 10 and – , not removable
e. 0, removable
____ 13. Find the x-values (if any) at which the function is not continuous.
Which of the discontinuities are removable?
a.
b.
c.
d.
e.
____ 14. Find the x-values (if any) at which is not continuous.
a.
b.
c.
d.
e.
1.4 Continuity and One-Sided Limits 73
____ 15. Find the constant a such that the function
is continuous on the entire real line.
a. 1
b.
c.
d.
e.
____ 16. Find the constants a and b 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.
____ 18. Find the value of c guaranteed by the Intermediate Value Theorem.
a.
b.
c.
d.
e.
74 Chapter 1: Limits and Their Properties
____ 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.
____ 20. Find all values of c such that is continuous on .
a.
b.
c.
d.
e.
1.4 Continuity and One-Sided Limits 75
1.4 Continuity and One-Sided Limits
Answer Section