1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

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Presentation transcript:

1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

Ex 1: Discontinuous where & why? *see graph.

1.4 Continuity  3 types of discontinuity: Removable Infinite Jump

a) b) Ex 2: Discontinuous where & why?

c) d) Ex 2: Discontinuous where & why?

Functions are continuous at every number in their domains!

 f is continuous on [a,b] if it is continuous on (a, b) and: Continuity on a Closed Interval

Ex 3: Show that f(x) is continuous on the interval [  1, 1]

Ex 4: Continuous where?

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.

Ex 5: Show that the equation has a root in the interval [1, 2]

pg – 5 odds, 7 – 23 EOO, 25 – 31 odds, 33 – 53 EOO, 57, 59, 75, 77, Total 1.4 pg – 5 odds, 7 – 23 EOO, 25 – 31 odds, 33 – 53 EOO, 57, 59, 75, 77, Total