F c for every sequence x n c in other words g f x g f

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f ( c ) for every sequence x n c . In other words, g f ( x ) g f ( c ) as x c , which means that the function g f ( x ) is continuous. Example. sin(1 + x 3 ) is continuous at every point x R because 1 + x 3 is continuous at all points x and sin y is continuous at all points y . 3
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