1. SECTION 2.4 Continuity & One-Sided Limits

2. Discontinuous v. Continuous

3. Formal Definition of Continuity Definition of Continuity (p. 90)

4. Two Types of Discontinuity

5. One-Sided Limits

6. When Does a Limit Exist? Theorem 2.10 The Existence of a Limit (p. 93)

7. Example 1 (#6)

8. Calculating One-Sided Limits 1. Plug in the x-value that you are approaching. 2. If you get a real number, then that’s your limit. 3. If not, try some algebra to see if things can cancel. 4. If that doesn’t work, then plug in x-values extremely close to the number you are approaching or graph it.

9. Example 2

10. Example 2 (cont.)

11. Continuity on a Closed Interval Definition of Continuity on a Closed Interval (p. 93)

12. Pictorial Representation

13. Example 3

14. Example 4

15. Example 5

16. Example 5 (cont.)

17. SECTION 2.5 Infinite Limits

18. Infinite Limits Defined

19. A Picture: An Example:

20. Infinite Limits

21. Vertical Asymptotes

22. Example 1

23. Example 2

24. Example 3

25. Example 4