52 Chapter 1: Limits and Their Properties
1.2 Finding Limits Graphically and Numerically
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Complete the table and use the result to estimate the limit.
x 2.9 2.99 2.999 3.001 3.01 3.1
a. 0.525000
b. 0.275000
c. –0.100000
d. 0.400000
e. –0.475000
____ 2. Complete the table and use the result to estimate the limit.
x 6.9 6.99 6.999 7.001 7.01 7.1
a. –0.062500
b. 0.067500
c. –0.192500
d. 0.047500
e. –0.172500
____ 3. Complete the table and use the result to estimate the limit.
x –0.1 –0.01 –0.001 0.001 0.01 0.1
a.
b.
c. 0
d. 0.5
e. 1
1.2 Finding Limits Graphically and Numerically 53
____ 4. Determine the following limit. (Hint: Use the graph to calculate the limit.)
a. 6
b. 1
c. 5
d. 4
e. does not exist
____ 5. Let
Determine the following limit. (Hint: Use the graph to calculate the limit.)
54 Chapter 1: Limits and Their Properties
a. 5
b. 4
c. 3
d. 0
e. does not exist
____ 6. Let
Determine the following limit. (Hint: Use the graph to calculate the limit.)
a. 6
b. 25
c. 1
d. 5
e. does not exist.
1.2 Finding Limits Graphically and Numerically 55
____ 7. Determine the following limit. (Hint: Use the graph to calculate the limit.)
a. –2
b. 0
c. –4
d. 2
e. does not exist
____ 8. A ring has a inner circumference of 10 centimeters. What is the radius of the ring?
Round your answer to four decimal places.
a. 0.7958 centimeter
b. 3.1831 centimeters
c. 1.5915 centimeters
d. 1.7841 centimeters
e. 10.1321 centimeters
____ 9. A ring has a inner circumference of 9 centimeters. If the ring’s inner circumference
can vary between 8 centimeters and 10 centimeters how can the radius vary? Round your answer to
five decimal places.
a. Radius can vary between 6.48456 centimeters and 10.13212 centimeters.
b. Radius can vary between 1.59577 centimeters and 1.78412 centimeters.
c. Radius can vary between 1.27324 centimeters and 1.59155 centimeters.
d. Radius can vary between 2.54648 centimeters and 3.18310 centimeters.
e. Radius can vary between 0.43239 centimeter and 2.43239 centimeters.
56 Chapter 1: Limits and Their Properties
____ 10. A sphere has a volume of 4.76 cubic inches. What is the radius of the sphere? Round
your answer to four decimal places.
a. 1.0435 inches
b. 1.6565 inches
c. 1.0660 inches
d. 2.1320 inches
e. 1.9335 inches
____ 11. A sphere has a volume of 4.44 cubic inches. If the sphere’s volume can vary between
3.64 cubic inches and 5.04 cubic inches , how can the radius vary? Round your answer to five
decimal places.
a. Radius can vary between 0.93219 inch and 1.09691 inches.
b. Radius can vary between 0.21960 inch and 1.61960 inches.
c. Radius can vary between 1.69081 inches and 1.98957 inches.
d. Radius can vary between 1.51481 inches and 1.68837 inches.
e. Radius can vary between 0.95427 inch and 1.06361 inches.
____ 12. Find the limit L.
a. L = 9
b. L = 2
c. L = 7
d. L = 16
e. none of the above
____ 13. Find the limit L.
a. L = 12
b. L = 6
c. L = 2
d. L = –4
e. none of the above
____ 14. What is the limit of as x approaches ?
a.
b.
c.
d.
e. none of the above
1.2 Finding Limits Graphically and Numerically 57
____ 15. The graph of is shown in the figure. Find such that if ,
then .
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
a.
b.
c.
d.
e. None of the above
58 Chapter 1: Limits and Their Properties
1.2 Finding Limits Graphically and Numerically
Answer Section
MULTIPLE CHOICE