Larson_Calculus_10e ch13sec02
MULTIPLE CHOICE
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.
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.
c.
d.
e.
6. Determine the continuity of the function .
a.
continuous except at
b.
continuous except at
c.
continuous except at
3
2
48
37
d.
continuous except at
e.
continuous everywhere
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.
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.
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 .
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
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.