1. Limits and Continuity
Section 2.3
Continuity

2. 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.

3. Continuity at a Point

4. Example Continuity at a Point

5. Continuity at a Point

6. Continuity at a Point

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

8. Continuity at a Point

10. Solution

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

12. Continuous Functions

13. Continuous Functions
[5,5] by [5,10]

14. Properties of Continuous Functions

15. Composite of Continuous Functions
Example

16. 1 2 3 4

17. Intermediate Value Theorem for Continuous Functions

18. Intermediate Value Theorem for Continuous Functions

19. Example

20. 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.

21. 1 2 3