lecture7-1_1 - 2.6 Continuity Continuity at a Point Example...

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2.6 Continuity Continuity at a Point Example 1 Consider y = f ( x ) below. Where is f continuous? Where is f discontinuous? What are the limits at these points? Continuous at every point in its domain [0 , 4] except at Discontinuous: 1
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Definitions Let y = f ( x ) be defined on the interval [ a, b ]. Interior point: A function y = f ( x ) is continuous at an interior point c of its domain if: Endpoint: A function y = f ( x ) is continuous at a left endpoint a or is continuous at a right endpoint b of its domain if: or respectively . If f is not continuous at a point c , we say that f is at c and say c is a point of discontinuity ( c need not be in the domain of f ). We say f is right-continuous (continuous from the right) at x = c if: We say f is left-continuous (continuous from the left) at x = c if: Example 2 f ( x ) = 4 - x 2 f is continuous at every point of its domain [ - 2 , 2]. f is right-continuous at and f is left-continuous at 2
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A function y = f ( x
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This note was uploaded on 03/31/2008 for the course MATH 1205 taught by Professor Fbhinkelmann during the Spring '08 term at Virginia Tech.

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lecture7-1_1 - 2.6 Continuity Continuity at a Point Example...

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