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Unformatted text preview: t ) . Every function from R to R 3 can be expressed as f ( t ) = ( f 1 ( t ) ,f 2 ( t ) ,f 3 ( t )) or f ( t ) = f 1 ( t ) + f 2 ( t ) + f 3 ( t ) k where f 1 ( t ), f 2 ( t ) and f 3 ( t ), the component Functions of f ( t ), are ordinary (real-valued) functions. Using Lemma 2.3.5 , it is easy to connect continuity of f ( t ) with continuity of its components: Remark 2.3.9. A function f : R R 3 is continuous on D R precisely if each of its components f 1 ( t ) , f 2 ( t ) , f 3 ( t ) is continuous on D . A related notion, that of limits, is an equally natural generalization of the single-variable idea:...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08