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Unformatted text preview: r (0) = h , 3 , 4 i ﬁnd the position at a general time t and when t = 1. Page 2 of 3 Total points this page out of 20 5. Assume r ( t ) = h t 3 , 5 , 2 t 2 i . (a) Find the arc length for 0 ≤ t ≤ 1 (b) Find the unit tangent vector T ( t ) for t > 0. (c) Find the curvature κ ( t ) at a general point t > 0. (d) Find the parametric equation of the tangent line to the curve when t = 1 6. Find the linear approximation of the function f ( x,y ) = (4 x 2 + y 2 ) 1 / 3 at (1 , 2) and use it to approximate f (1 . 05 , 1 . 95). You must give a computed numerical answer, a fraction is OK. Page 3 of 3 Total points this page out of 20...
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 Fall '08
 Keeran
 Calculus, Vector Space, Euclidean space

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