1.8 Continuity

1.8 Continuity - Continuity Section 1.8 Defn. of Continuity...

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Continuity Section 1.8
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Defn. of Continuity Continuity at a Point: A function f is continuous at c if the following 3 conditions are met. 1. f(c) is defined. 2. exists. 3. ) ( lim x f c x ) ( ) ( lim c f x f c x =
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Continuity on an Open Interval: A function is continuous on an open interval (a, b) if it is continuous at each point in the interval. A function that is continuous on the entire real line is everywhere continuous . ) , ( -∞
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Examples of graphs not continuous at x = c c f(c) is not defined does not exist c c ) ( lim x f c x ) ( ) ( lim c f x f c x
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Discontinuities Discontinuities fall into 2 categories: removable (tiny hole in graph – can be removed by canceling factors or by rationalizing) c
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nonremovable (gaps or asymptotes) c c
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One-Sided Limits & Continuity on a Closed Interval Limit from right Limit from left L x f c x = + ) ( lim L x f c x = - ) ( lim
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limits of functions involving radicals. For instance, if n is an even integer
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This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.

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1.8 Continuity - Continuity Section 1.8 Defn. of Continuity...

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