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Limit of a Composite Function

Limit of a Composite Function. If f and g are functions such that and , then. Example. Because and it follows that. Definition of Continuity.

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Limit of a Composite Function

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  1. Limit of a Composite Function If f and g are functions such that and , then

  2. Example Because and it follows that

  3. Definition of Continuity Continuity at a Point: A function f is continuous at cif the following three conditions are met. 1. f(c) is defined. 2. 3.

  4. Continuity 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. A function that is continuous on the entire real line is everywhere continuous.

  5. Continuity Continuity on a Closed Interval: A function f is continuous on a closed interval [a,b] if it is continuous on the open interval (a,b) and

  6. Intermediate Value Theorem If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c) = k.

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