1 / 13

Sec 4: CONTINUITY & ONE-SIDED LIMITS

Sec 4: CONTINUITY & ONE-SIDED LIMITS. I. Continuity. Definition of Continuity Continuity at a Point – A function f is continuous at a point if 1. f(c) is defined 2. exists 3. *see examples.

salim
Télécharger la présentation

Sec 4: CONTINUITY & 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. Sec 4: CONTINUITY & ONE-SIDED LIMITS

  2. I. Continuity • Definition of Continuity • Continuity at a Point – A function f is continuous at a point if 1. f(c) is defined 2. exists 3. *see examples

  3. Continuity on an Open Interval – A function is continuous on an open interval (a, b) if it is continuous at each point on the interval.

  4. II. Categories of Discontinuity • Removable - limit does exist at every point but is not continuous • Non-Removable – no limit at a point and is not continuous

  5. Ex 1: Identifying Continuity by Graphing • Tell is the function is continuous or discontinuous. If discontinuous, what kind. • A. B. C. D. y = sin x

  6. III. Testing for Continuity • Look for vertical asymptotes then tell the type of continuity or discontinuity. A. B. C.

  7. HOMEWORK • PG 76 #25-53 odds

  8. IV. One-Sided Limits • Limit from the right (positive side of graph) • Limit from the left (negative side of graph)

  9. Ex 2 • Find the limit of as x approaches -2 from the right. • Find the limit of as x approaches -2 from the left.

  10. III. Existence of a Limit • If and then

  11. Ex 3: Find the Limit (if it exists) A. B. C.

  12. Ex 4 • What do you do if you cannot show work algebraically to solve a one-sided limit?

  13. HOMEWORK • PG 76 #1-21 odds

More Related