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Unformatted text preview: p ( s ) = & 3 & s p 13 ± i + & 2 & s p 13 ± & 3 ± j = & 3 p 13 13 s i + 2 p 13 13 s & 3 ! j . 1 Please understand that the curves described by r and p are the same ! For example the portion of r that is traced out as t varies over the interval & 2 ± t ± 2 is the same as the portion of p that is traced out as s varies over the interval & 2 p 13 ± t ± 2 p 13 . What is &special±about the parameter s is that it corresponds to the actual distance travelled along the curve (beginning from the point (6 ; & 7) ) in travelling to the point whose position vector is p ( s ) . 2...
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 Fall '10
 Ellermeyer
 Math, Arc Length

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