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1-4 Continuity and One Sided Limits Notes

# 1-4 Continuity and One Sided Limits Notes -...

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1­4 Continuity and One Sided Limits Notes 2012 1 1.4 Determining Continuity & One­Sided Limits Continuous : at x=c ... if there are no jumps, holes, or gaps at f(c). Not Continuous : at x=c on (a,b) 1) 2) 3) a b c a b c a b c f undefined at c not continuous at c f defined at c not continuous at c f defined at c but not continuous at c open interval

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1­4 Continuity and One Sided Limits Notes 2012 2 Definition of Continuity (at a point) 1) f(c)is defined x c 2) lim f(x) exists 3) lim f(x) = f(c) x c The function f(x) is continuous at x=c if: Definition: A function f is continuous on an open interval (a,b) if it is continuous at every point in (a,b).
1­4 Continuity and One Sided Limits Notes 2012 3 Functions are discontinuous at vertical asymptotes, holes, and breaks in their graphs. Holes occur where a factor in the denominator of a fraction simplifies with a factor in the numerator of a fraction. This type of discontinuity is removeable.

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