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Chapter 2 Limits and Continuity Section 2.3 Continuity.

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Presentation on theme: "Chapter 2 Limits and Continuity Section 2.3 Continuity."— Presentation transcript:

1 Chapter 2 Limits and Continuity Section 2.3 Continuity

2 Quick Review

3 Quick Review

4 Quick Review

5 Quick Review

6 Quick Review Solutions

7 Quick Review Solutions

8 Quick Review Solutions

9 Quick Review Solutions

10 What you’ll learn about
Definition of continuity at a point Types of discontinuities Sums, differences, products, quotients, and compositions of continuous functions Common continuous functions Continuity and the Intermediate Value Theorem …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 Continuity at a Point

12 Example Continuity at a Point

13 Continuity at a Point

14 Continuity at a Point

15 Continuity at a Point The typical discontinuity types are:
Removable (2.21b and 2.21c) Jump (2.21d) Infinite (2.21e) Oscillating (2.21f)

16 Continuity at a Point

17 Example Continuity at a Point
[5,5] by [5,10]

18 Continuous Functions

19 Continuous Functions [5,5] by [5,10]

20 Properties of Continuous Functions

21 Composite of Continuous Functions

22 Intermediate Value Theorem for Continuous Functions

23 Intermediate Value Theorem for Continuous Functions

24 Intermediate Value Theorem for Continuous Functions
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.

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