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1.4 Continuity f is continuous at a if 1. is defined. 2. exists. 3.
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Ex 1: Discontinuous where & why? *see graph.
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1.4 Continuity 3 types of discontinuity: Removable Infinite Jump
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a) b) Ex 2: Discontinuous where & why?
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c) d) Ex 2: Discontinuous where & why?
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Functions are continuous at every number in their domains!
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f is continuous on [a,b] if it is continuous on (a, b) and: Continuity on a Closed Interval
![ f is continuous on [a,b] if it is continuous on (a, b) and: Continuity on a Closed Interval](http://images.slideplayer.com/26/8735275/slides/slide_7.jpg " f is continuous on [a,b] if it is continuous on (a, b) and: Continuity on a Closed Interval")
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Ex 3: Show that f(x) is continuous on the interval [ 1, 1]
![Ex 3: Show that f(x) is continuous on the interval [ 1, 1]](http://images.slideplayer.com/26/8735275/slides/slide_8.jpg "Ex 3: Show that f(x) is continuous on the interval [ 1, 1]")
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Ex 4: Continuous where?
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The Intermediate Value Theorem (IVT): If f is continuous on the interval [a, b] and k is any number between f(a) & f(b), then there exists a number c in (a, b) such that f(c) = k.
![The Intermediate Value Theorem (IVT): If f is continuous on the interval [a, b] and k is any number between f(a) & f(b), then there exists a number c in (a, b) such that f(c) = k.](http://images.slideplayer.com/26/8735275/slides/slide_10.jpg "The Intermediate Value Theorem (IVT): If f is continuous on the interval [a, b] and k is any number between f(a) & f(b), then there exists a number c in (a, b) such that f(c) = k.")
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Ex 5: Show that the equation has a root in the interval [1, 2]
![Ex 5: Show that the equation has a root in the interval [1, 2]](http://images.slideplayer.com/26/8735275/slides/slide_11.jpg "Ex 5: Show that the equation has a root in the interval [1, 2]")
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pg. 78 1 – 5 odds, 7 – 23 EOO, 25 – 31 odds, 33 – 53 EOO, 57, 59, 75, 77, 85 23 Total 1.4 pg. 78 1 – 5 odds, 7 – 23 EOO, 25 – 31 odds, 33 – 53 EOO, 57, 59, 75, 77, 85 23 Total
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