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Understanding Continuity and One-Sided Limits in Functions

Learn about continuity in functions, types of discontinuities, one-sided limits, Intermediate Value Theorem, and more. Practice problems included.

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Understanding Continuity and One-Sided Limits in Functions

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  1. Lesson 1.4Continuity and One-Sided Limits

  2. Continuity For every value, c, of a function; there is no interruption in the graph of f(c). There are no holes, gaps, or jumps Discontinuous

  3. Removable & Non-removable discontinuity Removable: we could write an equivalent function that is continuous Non-removable: no limit would exist

  4. Example 1

  5. One-Sided Limits *For functions with no limit at c Right sided limit: Left sided limit: Limit from the right. Limit from the left.

  6. Example 2

  7. Intermediate Value Theorem Mainly used to test for “zeros”: If f(a) > 0 and f(b) < 0, and f is continous between a and b then we there must be a value where the function is 0.

  8. Example 3

  9. Other Function Continuity Properties

  10. Example 4 Problem Set 1.4

  11. Continuity on a Closed Interval

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