3.5 Limits at Infinity 179
3.5 Limits at Infinity
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Match the function with one of the following graphs.
a. d.
b. e.
c.
180 Chapter 3: Applications of Differentiation
____ 2. Match the function with one of the following graphs.
a. d.
b. e.
c.
3.5 Limits at Infinity 181
____ 3. Match the function with one of the following graphs.
a. d.
b. e.
c.
182 Chapter 3: Applications of Differentiation
____ 4. For the function , use a graphing utility to complete the table and
estimate the limit as x approaches infinity.
a. 0.8000
b. 1.8000
c. 1.2500
d. 2.2500
e. 0.2500
____ 5. For the function , use a graphing utility to complete the table and
estimate the limit as x approaches infinity.
a. –0.2500
b. 1.0000
c. 2.1800
d. –0.9000
e. does not exist
____ 6. For the function , use a graphing utility to complete the table and
estimate the limit as x approaches infinity.
a. –6
b 2
c. 6
d. 0
e. None of the above
3.5 Limits at Infinity 183
____ 7. Find the limit.
a.
b. 3
c.
d. –3
e. 5
____ 8. Find the limit.
a. 1
b. 0
c.
d.
e. does not exist
____ 9. Find the limit.
a.
b. 1
c. 0
d.
e.
184 Chapter 3: Applications of Differentiation
____ 10. Find the limit.
a.
b.
c. 1
d. –6
e.
____ 11. Find the limit.
a.
b.
c. 1
d. 7
e.
3.5 Limits at Infinity 185
____ 12. Sketch the graph of the function using any extrema, intercepts,
symmetry, and asymptotes.
a. d.
b. e.
c.
186 Chapter 3: Applications of Differentiation
____ 13. Sketch the graph of the function using any extrema, intercepts,
symmetry, and asymptotes.
a. d.
b. e.
c.
3.5 Limits at Infinity 187
____ 14. Sketch the graph of the relation using any extrema, intercepts, symmetry,
and asymptotes.
a. d.
b. e.
c.
188 Chapter 3: Applications of Differentiation
____ 15. Sketch the graph of the relation using any extrema, intercepts, symmetry,
and asymptotes.
a. d.
b. e.
c.
3.5 Limits at Infinity 189
____ 16. A business has a cost of for producing x units. The average cost per
unit is Find the limit of as x approaches infinity.
a. 333.3
b. 1
c. 500
d. 0
e. 1.5
____ 17. The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds
after it is removed from a kiln.
Find .
a.
b.
c.
d.
e.
____ 18. A model for the average typing speeds S (words per minute) of a typing student after
t weeks of lessons is given by Find .
a. 96 words per minute
b. 12 words per minute
c. 56 words per minute
d. 162 words per minute
e. 81 words per minute
190 Chapter 3: Applications of Differentiation
____ 19. A heat probe is attached to the heat exchanger of a heating system. The temperature T
(in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded
for the first two minutes is given by . Find .
a.
b.
c.
d.
e.
3.5 Limits at Infinity 191
3.5 Limits at Infinity
Answer Section
MULTIPLE CHOICE