494 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.7 Indeterminate Forms and L’Hôpital’s Rule
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the limit first by using techniques from Chapter 1 then by
using L’Hopital’s Rule.
a.
b.
c.
d. 0
e. does not exist
____ 2. Evaluate the limit first by using techniques from Chapter 1 then
by using L’Hopital’s Rule.
a.
b. 0
c.
d.
e. does not exist
____ 3. Evaluate the limit first by using techniques from Chapter 3 then
by using L’Hopital’s Rule.
a.
b.
c.
d.
e. does not exist
8.7: Indeterminate Forms and L’Hôpital’s Rule 495
____ 4. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c. 1
d. 0
e. does not exist
____ 5. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d. 0
e.
____ 6. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b. 0
c.
d.
e. does not exist
____ 7. Evaluate the using L’Hôpital’s Rule if necessary.
a.
b.
c.
d. 0
e.
496 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 8. Evaluate the using L’Hôpital’s Rule if necessary.
a.
b.
c.
d.
e. 0
____ 9. Evaluate the limit using L’Hopital’s Rule if necessary.
a. 0
b.
c.
d. 1
e. does not exist
____ 10. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d.
e. 0
____ 11. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d. 0
e.
8.7: Indeterminate Forms and L’Hôpital’s Rule 497
____ 12. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d.
e.
____ 13. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d. 0
e. does not exist
____ 14. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c. 1
d.
e.
____ 15. Evaluate the limit using L’Hopital’s Rule if necessary.
a. 1
b.
c. 0
d.
e.
498 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 16. Evaluate the limit using L’Hopital’s Rule if necessary.
a.
b.
c.
d.
e. does not exist
____ 17. Apply the Extended Mean Value Theorem to the functions and
on the interval , and find all values c in the interval such that
.
a.
b.
c.
d.
e.
83
8.7: Indeterminate Forms and L’Hôpital’s Rule 499
8.7 Indeterminate Forms and L’Hôpital’s Rule
Answer Section