14209an3.6-8

14209an3.6-8 - c Kendra Kilmer February 3, 2009 Section 3.2...

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Unformatted text preview: c Kendra Kilmer February 3, 2009 Section 3.2 - Continuity Definition: A function f is continuous at the point x = c if all of the following are true: 1. 2. 3. Note: If one or more of the conditions are not met, we say f is discontinuous at x = c. Example 1: For what values of x is the function discontinuous? Explain. 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 -1 -2 -3 -4 -5 -6 4 5 6 f(x) Definition: A function is continuous on the open interval (a, b) if it is continuous at each point on the interval. 6 c Kendra Kilmer February 3, 2009 Functions continuous for all real numbers: Functions continuous on their domain: Example 2: Find the intervals on which the following functions are continuous. a) f (x) = 3x9 + 4x5 - 7 b) g(x) = 23x + 4 c) h(x) = log8 (x - 3) - 2 d) k(x) = x+2 x2 - x - 12 x - 5 x + 2 e) m(x) = 2x2 x x-4 if x -3 if x > 0 if - 3 < x 0 7 c Kendra Kilmer February 3, 2009 Example 3: Find the value(s) of k, if any exist, that will make f (x) continuous everywhere. f (x) = 2x - 5 x2 + k if x 1 if x > 1 Section 3.2 Homework Problems: 3-11(odd), 15-25(odd),35,37,41,43,45,51,53,63,65,71,79 and supplemental problems 8 ...
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This note was uploaded on 03/27/2012 for the course MATH 142 taught by Professor Drost during the Fall '08 term at Texas A&M.

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14209an3.6-8 - c Kendra Kilmer February 3, 2009 Section 3.2...

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