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 ) −→ ı + 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 (realvalued) 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 singlevariable idea:...
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 Fall '08
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 Calculus, Derivative, Continuous function, Limit of a sequence

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