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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.

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Sec 4: CONTINUITY & ONE-SIDED LIMITS

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  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

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