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2_6 Continuity -Hass_ppt [Compatibility Mode]

# 2_6 Continuity -Hass_ppt [Compatibility Mode] - Definition...

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8/31/2009 1 Continuity Section 2.6 Definition of Continuity A function is continuous at c if the following three conditions are met: 1. is defined 2. exists 3. ) ( c f ) ( lim x f c x ) ( ) ( lim c f x f c x = Examples: Use the definition of continuity to determine if the following function is continuous at 1. Use the definition of continuity to determine if the following function is continuous at 1. + < + = 1 , 1 1 , 1 ) ( 3 x x x x x f - = 1 , 1 1 , ) ( x x x x x f Types of Discontinuities Removable (Holes in the graph) Nonremovable Infinite Finite Jump Continuity on Intervals A function is continuous on an open interval (a,b) if it is continuous at each point in the interval. A function is continuous on a closed interval [a,b] if it is continuous on the open interval (a,b) and and . (i.e., nothing "bad" happens at the endpoints) We say a function is continuous if it is continuous on the entire real line.

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