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Continuity in Mathematics

Learn about continuity at a point, types of discontinuities, continuous functions, and the Intermediate Value Theorem. Explore how continuous functions describe motion and reaction speed changes. Examples and properties included.

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Continuity in Mathematics

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  1. Continuity Chapter 2 Limits and Continuity Section 2.3

  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 o

  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 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 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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