1. Limits and Continuity
Chapter 2:

2. Aim #2.2 How do we solve limits as x approaches +/- infinity?
We use infinity when the values in its domain or range outgrow all finite bounds.
Graph y = 1/x
What happens as x approaches to + infinity?
What happens as x approaches to - infinity?

3. Definition: Horizontal Asymptote

4. Example 1: Looking for Horizontal Asymptotes

5. Graph the following f(x)

6. Theorem 5

7. Example 5: Using the Theorem 5

8. Infinite Limits as x ---a
Graph the function f(x)= 1/x. What happens as x approaches 0 from the right?
From the left?
What does y approach?

9. Definition: Vertical Asymptotes

10. Example 4: Finding the Vertical Asymptote
What does f(x) approach as x approaches 0 from the right? From the left?

11. Example 5: Finding Vertical Asymptotes
What are the vertical asymptotes of
f(x)= tan x?

12. End Behavior Models
For numerically large values of x, we can sometimes model the behavior of a complicated function by a simpler one that acts virtually the same way.

13. Example 6:

14. Definition End Behavior Models

15. Example 7:

16. Seeing Limits as x approaches +/- infinity
We can investigate the graph of y =f(x) as x approaches +/- infinity by investigating the graph of y =f(1/x) as x approaches infinity.

17. Example 9: Using Substitution

18. Summary: Answer in complete sentences.
Explain why there is no value L for which lim as x approaches infinity for sin x = L