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Unformatted text preview: v r ( t ) = < 30 t 4 , 12 t 2 , 2 > = 2 < 15 t 3 , 6 t 2 , 1 >, and v r (1) = 2 < 15 , 6 , 1 >, so the length  v r (1)  = 2 225 + 36 + 1 = 2 262 , so v T (1) = 1 262 < 15 , 6 , 1 > . Note that fnding v T ( t ) frst, beore setting t = 1 , makes the problem harder; while setting t = 1 in v r ( t ) beore dierentiating changes the derivative to v 0 : the above steps are in exactly the correct order to get the right answer with least computation....
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 Spring '06
 YUKICH
 Calculus, Arc Length, Derivative

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