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Unformatted text preview: Â±v Â· Â±v =1. (c) Three lines that are mutually skewed to each other. (d) Three noncoplanar points. 4. (10 pts) Show that lim ( x,y ) â†’ (0 , 0) y 2 x 3 + y 3 + 2 xy doesnâ€™t exist. 5. (10 pts) Find lim ( x,y ) â†’ (0 , 0) x 3 x 2 + y 2 and justify your answer. 6. (10 pts) For the curve Â± r ( t ) = (3 tt 3 , 3 t 2 , 3 t + t 3 ), compute at the point (0 , , 0) the curvature Îº , the unit tangent vector Â± T and the unit normal vector Â± N . 7. (10 pts) Find the distance between the plane of equation x + y + z = 1 and the point P = (0 , , 2). 8. (10 pts) Compute the following partial derivatives. (a) âˆ‚ âˆ‚x â€¡ x 2 + xy + e 3 xz Â· = (b) âˆ‚ âˆ‚z â€¡ z sin ( x + y ) + y 2007 x Â· = 2...
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 Spring '08
 HAIN
 Calculus, Euclidean space, Duke University

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