1. Chapter 2  2012 Pearson Education, Inc. 2.2 Limits Involving Infinity Section 2.2 Limits and Continuity

2. Slide 2.2- 2  2012 Pearson Education, Inc. Quick Review

3. Slide 2.2- 3  2012 Pearson Education, Inc. Quick Review

4. Slide 2.2- 4  2012 Pearson Education, Inc. Quick Review

5. Slide 2.2- 5  2012 Pearson Education, Inc. Quick Review

6. Slide 2.2- 6  2012 Pearson Education, Inc. Quick Review Solutions [  12,12] by [  8,8][  6,6] by [  4,4]

7. Slide 2.2- 7  2012 Pearson Education, Inc. Quick Review Solutions

8. Slide 2.2- 8  2012 Pearson Education, Inc. Quick Review Solutions

9. Slide 2.2- 9  2012 Pearson Education, Inc. Quick Review Solutions

10. Slide 2.2- 10  2012 Pearson Education, Inc. What you’ll learn about  Finite Limits as x→±∞  Sandwich Theorem Revisited  Infinite Limits as x→a  End Behavior Models  Seeing Limits as x→±∞ …and why Limits can be used to describe the behavior of functions for numbers large in absolute value.

11. Slide 2.2- 11  2012 Pearson Education, Inc. Finite limits as x→±∞ The symbol for infinity (∞) does not represent a real number. We use ∞ to describe the behavior of a function when the values in its domain or range outgrow all finite bounds. For example, when we say “the limit of f as x approaches infinity” we mean the limit of f as x moves increasingly far to the right on the number line. When we say “the limit of f as x approaches negative infinity (  ∞)” we mean the limit of f as x moves increasingly far to the left on the number line.

12. Slide 2.2- 12  2012 Pearson Education, Inc. Horizontal Asymptote

13. Slide 2.2- 13  2012 Pearson Education, Inc. [-6,6] by [-5,5] Example Horizontal Asymptote

14. Slide 2.2- 14  2012 Pearson Education, Inc. Example Sandwich Theorem Revisited

15. Slide 2.2- 15  2012 Pearson Education, Inc. Properties of Limits as x→±∞

16. Slide 2.2- 16  2012 Pearson Education, Inc. Properties of Limits as x→±∞

17. Slide 2.2- 17  2012 Pearson Education, Inc. Properties of Limits as x→±∞

18. Slide 2.2- 18  2012 Pearson Education, Inc. Infinite Limits as x→a

19. Slide 2.2- 19  2012 Pearson Education, Inc. Vertical Asymptote

20. Slide 2.2- 20  2012 Pearson Education, Inc. Example Vertical Asymptote [  6,6] by [  6,6]

21. Slide 2.2- 21  2012 Pearson Education, Inc. End Behavior Models

22. Slide 2.2- 22  2012 Pearson Education, Inc. Example End Behavior Models

23. Slide 2.2- 23  2012 Pearson Education, Inc. End Behavior Models

24. Slide 2.2- 24  2012 Pearson Education, Inc. End Behavior Models

25. Slide 2.2- 25  2012 Pearson Education, Inc. Example “Seeing” Limits as x→±∞

26. Slide 2.2- 26  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

27. Slide 2.2- 27  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

28. Slide 2.2- 28  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

29. Slide 2.2- 29  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

30. Slide 2.2- 30  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

31. Slide 2.2- 31  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2