One way to parametrize the cyclists path is t 2 t cos

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Unformatted text preview: that F is conservative with potential function g (x, y, z ) = xy + z . Hence the work done is independant 2π of the path chosen. Work done is W = F · ds = 0 √ g (B ) − g (A) = g (0, 0, 2π ) − g ( 2π, 0, 0) = 2π − 0 = 2π . One way to √ parametrize √ the cyclist’s path is γ (t) = 2π − t cos t, 2π − t sin t, t , 0 ≤ t ≤ 2π . This gives her velocity as γ (t) = cos t + 2 (2π − t) sin t 2 (2π − t) cos t − sin t √ √ − , ,1 2 2π − t 2 2π − t 1 − 4π − 2t . As she approaches the top of and her speed as √ 2 2π − t 1 − 4π − 2t the hill her speed is represented by lim− √ = ∞. t→2π 2 2π − t Clearly this i...
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This document was uploaded on 03/17/2014 for the course MAT B42 at University of Toronto.

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