AB_limits_lesson_14_part_2

AB_limits_lesson_14_part_2 - 8/29/2011 Calculus AP-AB...

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8/29/2011 1 Calculus AP-AB August 29, 2011 Section 1.4 Definition of Continuity Continuity at a point: A function f is continuous at x = c, if 3 conditions are met. 1. f(c) exists 2. f(x) exists 3. f(x) = f(c) c x lim c x lim
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8/29/2011 2 Objective: Determine continuity Does the function exist? Does the limit exist? Are they equal? If all three aren’t true at a point, the function is discontinuous at that point. Removable vs. nonremovable Does the function exist? Find the domain of the function Polynomials are continuous everywhere Rational functions exist everywhere the denominator is not zero Piecewise functions exist everywhere they are defined
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8/29/2011 3 Does the limit exist? Is the limit from the left equal to the limit from the right for all x? Types of discontinuities Removable – becomes continuous by redefining the function at a single point (hole) Non-removable – cannot become continuous (vertical asymptote)
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This note was uploaded on 09/19/2011 for the course CALCULUS 1431 taught by Professor All during the Fall '11 term at University of Houston.

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AB_limits_lesson_14_part_2 - 8/29/2011 Calculus AP-AB...

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