1. Limits Involving Infinity
Chapter 2
Limits and Continuity
Section 2.2
Limits Involving Infinity

2. Quick Review

3. Quick Review

4. Quick Review

5. Quick Review

6. Quick Review Solutions
[12,12] by [8,8]
[6,6] by [4,4]

7. Quick Review Solutions

8. Quick Review Solutions

9. Quick Review Solutions

10. What you’ll learn about
The Squeeze Theorem for limits at infinity
Asymptotic and unbounded behavior of functions
End behavior of functions
…and why
Limits can be used to describe the behavior of functions
for numbers large in absolute value.

11. 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. Horizontal Asymptote

13. Example Horizontal Asymptote
[-6,6] by [-5,5]

14. Example Sandwich Theorem Revisited

15. Properties of Limits as x→±∞

16. Properties of Limits as x→±∞

17. Properties of Limits as x→±∞

18. Infinite Limits as x→a

19. Vertical Asymptote

20. Example Vertical Asymptote

21. End Behavior Models

22. End Behavior Models

23. Example End Behavior Models

24. End Behavior Models

25. Example “Seeing” Limits as x→±∞

26. Quick Quiz Sections 2.1 and 2.2

27. Quick Quiz Sections 2.1 and 2.2

28. Quick Quiz Sections 2.1 and 2.2

29. Quick Quiz Sections 2.1 and 2.2

30. Quick Quiz Sections 2.1 and 2.2

31. Quick Quiz Sections 2.1 and 2.2