Lesson 5 Continuity - CONTINUITY Objectives At the end of...

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CONTINUITY
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Objectives At the end of the discussion, the students, at the minimum, would be able to: - Discuss the concept of continuity - Verify whether a given function is continuous at a given value of x. - Classify the nature of discontinuity of a given function.
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Definition 1.5.1 (p. 110) If one or more of the above conditions fails to hold at C the function is said to be discontinuous . DEFINITION: CONTINUITY OF A FUNCTION
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Theorem 1.5.3 (p. 113)
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Question 8 EXAMPLE Solution : ( 29 ( 29 ( 29 2 2 3 6 3 x x x x f x x + - - - = = - 3 x - ( 29 2 2 3 x f x x where x = + = - 1. Given the function f defined as , draw a sketch of the graph of f, then by observing where there are breaks in the graph, determine the values of the independent variable at which the function is discontinuous and why each is discontinuous. ( 29 2 6 3 x x f x x - - = -
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y x Test for continuity: at x=3 1. f(3) is not defined; since the first condition is not satisfied then f is discontinuous at x=3.
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Lesson 5 Continuity - CONTINUITY Objectives At the end of...

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