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750 Chapter 13: Functions of Several Variables
13.2 Limits and Continuity
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find by using the limits and
.
a.
b.
c.
d.
e.
____ 2. Find by using the limits and
.
a.
b.
c.
d.
e.
____ 3. Find the limit.
a.
b.
c.
d.
e.
13.2 Limits and Continuity 751
____ 4. Determine the continuity of the function .
a. continuous except at
b. continuous except at
c. continuous except at
d. continuous except at
e. continuous everywhere
____ 5. Find the limit .
a.
b.
3
2
c.
48
37
d.
e.
____ 6. Determine the continuity of the function .
a. continuous except at
b. continuous except at
c. continuous except at
d. continuous except at
e. continuous everywhere
752 Chapter 13: Functions of Several Variables
____ 7. Find the limit.
a.
b.
c.
d.
e.
____ 8. Determine the continuity of the function .
a. continuous except at
b. continuous except at
c. continuous for all
d. continuous for all
e. continuous everywhere
____ 9. Find the limit.
a.
b.
c.
d.
e.
13.2 Limits and Continuity 753
____ 10. Find the limit.
a.
b.
c.
d.
e.
____ 11. Use polar coordinates to find the limit. [Hint: Let and , and note
that implies .]
a.
b.
c.
d.
e. limit does not exist
____ 12. Use polar coordinates to find the limit . [Hint: Let
and , and note that implies .]
a.
b.
c.
d.
e.
754 Chapter 13: Functions of Several Variables
____ 13. Use polar coordinates and L'Hopital's Rule to find the limit.
a.
b.
c.
d.
e.
____ 14. Determine the continuity of the function .
a. continuous except at
b. continuous for
c. continuous except at
d. continuous except at
e. continuous for
____ 15. Discuss the continuity of the function.
a. is continuous everywhere except at those points such that .
b. is continuous everywhere except at those points such that .
13.2 Limits and Continuity 755
c. is continuous at those points such that .
d. is continuous only when .
e. is continuous everywhere in the xy-plane.
____ 16. Determine the continuity of the composite function where and
.
a. continuous except at
b. continuous for all
c. continuous for all
d. continuous except at
e. continuous everywhere
____ 17. Find the limit for the function .
a. –5y
b.
c.
d. 5y
e. 8x
____ 18. Find the limit for the function .
a.
b. –6
c.
d. 16x
e. 6y
756 Chapter 13: Functions of Several Variables
____ 19. Find the limit for the function .
a.
b.
c.
d.
e. –5y
____ 20. Find the limit for the function .
a.
b.
c.
d.
e.
____ 21. Use spherical coordinates to find the limit
[Hint: Let and , and note that implies
.]
a. 6
b. 9
c. 1
d. 7
e.
13.2 Limits and Continuity 757
13.2 Limits and Continuity
Answer Section
MULTIPLE CHOICE
