1 / 17

1.6

1.6. Techniques for Computing Limits: The Limit Laws. Computing Limits. Basic Limits : For real numbers b and c, and positive integers n:. Properties of Limits. Properties of Limits (continued). Methods for Computing Limits. A. “Plug-Ins” (Direct substitution)

brinda
Download Presentation

1.6

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. 1.6 Techniques for Computing Limits: The Limit Laws

  2. Computing Limits Basic Limits: For real numbers b and c, and positive integers n:

  3. Properties of Limits

  4. Properties of Limits (continued)

  5. Methods for Computing Limits • A. “Plug-Ins” (Direct substitution) • Using these basic limits and properties of limits, we can prove that the limit at c of the following kinds of functions can be evaluated by direct substitution of c for x. • Direct substitution will work for: • Polynomial Functions • Rational Functions with c in domain • Radical Functions with c in domain • Trigonometric Functions with c in its domain

  6. Examples

  7. Methods for Computing Limits B. Rational Functions with c not in domain(“Single Holes”)

  8. -

  9. Example 4

  10. C. Functions with radicals, c not in domain:

  11. D. Special Trigonometric Limits Theorems:

  12. Examples:

  13. The Squeeze Theorem

  14. Example (using the Squeeze Theorem):

More Related