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Unformatted text preview: MAC 2233/001006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Assistants : Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing han Meng Brief notes on continuity Informally, a function is continuous at x = c means that the graph of the function is continuous (that is, not broken, no gap, no hole, no jump) at x = c . Therefore, a function f is continuous at x = c if lim x → c f ( x ) = f ( c ) . That is, f is continuous at x = c provided the following THREE conditions are satisfied: (1) f ( c ) is defined, (2) lim x → c f ( x ) exists, and (3) the value of the limit equals f ( c ). Consider the graph of the function y = f ( x ) below as an example throughout this note. Using the above graph as an example, we see that (a) f is continuous at x = 2, (b) f is not continuous at x = − 1 since f ( − 1) is not defined, (c) f is not continuous at x = 0 since f (0) is not defined (and since lim x → f ( x ) does not exist), (d) f is not continuous at...
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.
 Fall '08
 DANIELYAN
 Calculus, Continuity

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