1. Chapter 2  2012 Pearson Education, Inc. 2.3 Section 2.3 Continuity Limits and Continuity

2. Slide 2.3- 2  2012 Pearson Education, Inc. Quick Review

3. Slide 2.3- 3  2012 Pearson Education, Inc. Quick Review

4. Slide 2.3- 4  2012 Pearson Education, Inc. Quick Review

5. Slide 2.3- 5  2012 Pearson Education, Inc. Quick Review

6. Slide 2.3- 6  2012 Pearson Education, Inc. Quick Review Solutions

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9. Slide 2.3- 9  2012 Pearson Education, Inc. Quick Review Solutions

10. Slide 2.3- 10  2012 Pearson Education, Inc. What you’ll learn about  Continuity at a Point  Continuous Functions  Algebraic Combinations  Composites  Intermediate Value Theorem for Continuous Functions …and why Continuous functions are used to describe how a body moves through space and how the speed of a chemical reaction changes with time.

11. Slide 2.3- 11  2012 Pearson Education, Inc. Continuity at a Point

12. Slide 2.3- 12  2012 Pearson Education, Inc. Example Continuity at a Point o

13. Slide 2.3- 13  2012 Pearson Education, Inc. Continuity at a Point

14. Slide 2.3- 14  2012 Pearson Education, Inc. Continuity at a Point

15. Slide 2.3- 15  2012 Pearson Education, Inc. Continuity at a Point The typical discontinuity types are: a)Removable(2.21b and 2.21c) b)Jump (2.21d) c)Infinite(2.21e) d)Oscillating (2.21f)

16. Slide 2.3- 16  2012 Pearson Education, Inc. Continuity at a Point

17. Slide 2.3- 17  2012 Pearson Education, Inc. Example Continuity at a Point [  5,5] by [  5,10]

18. Slide 2.3- 18  2012 Pearson Education, Inc. Continuous Functions

19. Slide 2.3- 19  2012 Pearson Education, Inc. Continuous Functions [  5,5] by [  5,10]

20. Slide 2.3- 20  2012 Pearson Education, Inc. Properties of Continuous Functions

21. Slide 2.3- 21  2012 Pearson Education, Inc. Composite of Continuous Functions

22. Slide 2.3- 22  2012 Pearson Education, Inc. Intermediate Value Theorem for Continuous Functions

23. Slide 2.3- 23  2012 Pearson Education, Inc. The Intermediate Value Theorem for Continuous Functions is the reason why the graph of a function continuous on an interval cannot have any breaks. The graph will be connected, a single, unbroken curve. It will not have jumps or separate branches. Intermediate Value Theorem for Continuous Functions