CALCULUS CHAPTER 1 Section 1.4: Continuity and One-Sided Limits Calculus Chapter 1 Section 4 1.

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Presentation transcript:

CALCULUS CHAPTER 1 Section 1.4: Continuity and One-Sided Limits Calculus Chapter 1 Section 4 1

CONTINUITY AT A POINT AND ON AN OPEN INTERVAL In mathematics the term continuous has much the same meaning as it has in everyday usage. To say a function is continuous means that it contains no holes, jumps, or gaps. Calculus Chapter 1 Section 4 2

CONTINUITY AT A POINT AND ON AN OPEN INTERVAL Calculus Chapter 1 Section 4 3

DEFINITION OF CONTINUITY Calculus Chapter 1 Section 4 4

ONE-SIDED LIMITS AND CONTINUITY ON A CLOSED INTERVAL Calculus Chapter 1 Section 4 5

ONE-SIDED LIMITS AND CONTINUITY ON A CLOSED INTERVAL Calculus Chapter 1 Section 4 6

THEOREM 1.10: THE EXISTENCE OF A LIMIT Calculus Chapter 1 Section 4 7

DEFINITION OF CONTINUITY ON A CLOSED INTERVAL Calculus Chapter 1 Section 4 8

THEOREM 1.11: PROPERTIES OF CONTINUITY Calculus Chapter 1 Section 4 9

THEOREM 1.12: CONTINUITY OF A COMPOSITE FUNCTION Calculus Chapter 1 Section 4 10

THEOREM 1.13: INTERMEDIATE VALUE THEOREM Calculus Chapter 1 Section 4 11

HOMEWORK Page 76 #5-52, #59-70 GRADED PORTION: ##6, #10, #14, #20, #30, #36, #46, #60 DUE DATE: 11/17/2015 Calculus Chapter 1 Section 4 12

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