1. 2.2 Limits Involving Infinity

2. 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.

3. 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.

4. Horizontal Asymptote

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

6. Example Sandwich Theorem Revisited

7. Properties of Limits as x→±∞

8. Product Rule: Constant Multiple Rule:

9. Properties of Limits as x→±∞

10. Infinite Limits as x→a

11. Vertical Asymptote

12. Example Vertical Asymptote [-6,6] by [-6,6]

13. End Behavior Models

14. Example End Behavior Models

15. End Behavior Models

17. Example “Seeing” Limits as x→±∞