1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.2 L’Hôpital’s Rule

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 3 Quick Review

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 4 Quick Review Solutions

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 5 Quick Review Solutions

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 6 What you’ll learn about Indeterminate Form 0/0 Indeterminate Forms ∞/∞, ∞·0, ∞-∞ Indeterminate Form 1 ∞, 0 0, ∞ 0 …and why Limits can be used to describe the behavior of functions and l’Hôpital’s Rule is an important technique for finding limits.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 7 Indeterminate Form 0/0

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 8 L’Hôpital’s Rule (First Form)

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 9 Example Indeterminate Form 0/0

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 10 L’Hôpital’s Rule (Stronger Form)

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 11 Example Using L’Hôpital’s Rule with One-Sided Limits

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 12 Example Working with Indeterminate Form ∞/∞

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 13 Example Working with Indeterminate Form ∞·0

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 14 Indeterminate Forms 1 ∞, 0 0,∞ 0

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 15 Example Working with Indeterminate Form 1 ∞

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 16 Example Working with Indeterminate Form 1 ∞

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 17 Example Working with Indeterminate Form 0 0

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 18 Example Working with Indeterminate Form ∞ 0

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 19 Quick Quiz for Sections 8.1 and 8.2

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 20 Quick Quiz for Sections 8.1 and 8.2

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 21 Quick Quiz for Sections 8.1 and 8.2

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 22 Quick Quiz for Sections 8.1 and 8.2

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 23 Quick Quiz for Sections 8.1 and 8.2

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 8- 24 Quick Quiz for Sections 8.1 and 8.2