1 / 11

Lesson 1.4 Continuity and One-Sided Limits

Lesson 1.4 Continuity and One-Sided Limits. 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. Removable & Non-removable discontinuity

tberg
Download Presentation

Lesson 1.4 Continuity and One-Sided Limits

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related