Continuity and One-Sided Limits

Continuity and One-Sided Limits - Continuity and One-Sided...

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Continuity and Continuity and One-Sided Limits One-Sided Limits Section 1.4
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Defn. of Continuity 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 Examples of graphs not continuous at x = c continuous at x = c c f(c) is not defined ) ( lim x f c x does not exist c c ) ( ) ( lim c f x f c x
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Discontinuities 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 One-Sided Limits & Continuity on a Closed Interval on a Closed Interval L x f c x = + ) ( lim Limit from right L x f c x = - ) ( lim Limit from left
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One-sided limits are useful in taking limits of functions involving radicals. For instance, if n is an even integer 0 lim 0 = + n x x
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Thm. 1.10
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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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Continuity and One-Sided Limits - Continuity and One-Sided...

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