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Lecture 2_4 Ma 141

Lecture 2_4 Ma 141 - if each is continuous or not at x = 1...

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Outline of Lecture Section 2.4 – Continuity 1. Definition : First draw a continuous graph on your paper page 117 A function is continuous at x = a ) ( ) ( lim a f x f a x = 3 implied facts in this one statement How we define continuity over closed intervals? If we write f is continuous on the closed interval [a, b] then we mean that the function is continuous for every interior point on the interval while also being continuous from the right for lower endpoint a and continuous from the left for upper endpoint b. Example #4 page 126 Draw picture from the text (or board during class)
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Example – Given the following two piece-wise defined functions, f and g, decide
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Unformatted text preview: if each is continuous or not at x = 1? Graph the functions and discuss the difference in the functions. Theorem (p. 124) The Intermediate Value Theorem Suppose f is continuous on the closed interval [a, b] and N is any number between f(a) and f(b), where f(a) does not equal f(b). Then there exists a number c in (a ,b) such that f(c) = N. Picture: Example - #37 p.127 Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. 3 4 =-+ x x on the interval (1,2)...
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