1 / 13

1.4 Continuity and One-Sided Limits (Part 1)

Learn how to determine one-sided limits and continuity on a closed interval. Explore examples and considerations for rational, polynomial functions, even radicals, piecewise functions, and infinite limits. Practice problems included.

rconley
Download Presentation

1.4 Continuity and One-Sided Limits (Part 1)

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. 1.4 Continuity and One-Sided Limits(Part 1)

  2. Objectives • Determine one-sided limits and continuity on a closed interval.

  3. One-Sided Limits

  4. Example

  5. Two-Sided Limits • For most rational & polynomial functions: no difference in left, right or two-sided limits • Need to check both sides if: • Even radical (domain gap) • Piecewise functions • Absolute value • Infinite Limits (next section)

  6. Example For even radicals, evaluate the domain first. D: x-2≥0, x≥2 [2,∞)

  7. Example D: 1-x2≥0, x2≤1, |x|≤1, [-1,1]

  8. Examples Show domain on test!

  9. Example

  10. Example

  11. Greatest Integer Function

  12. Examples

  13. Homework 1.4 (page 76) #1-7 odd, #11-17 odd #21,23 Handout (2.5) #1-9 odd #21, 22, 24, 30, 44, 48, 49, 50, 52

More Related