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Unformatted text preview: v v =1. (c) Three lines that are mutually skewed to each other. (d) Three noncoplanar points. 4. (10 pts) Show that lim ( x,y ) (0 , 0) y 2 x 3 + y 3 + 2 xy doesnt exist. 5. (10 pts) Find lim ( x,y ) (0 , 0) x 3 x 2 + y 2 and justify your answer. 6. (10 pts) For the curve r ( t ) = (3 tt 3 , 3 t 2 , 3 t + t 3 ), compute at the point (0 , , 0) the curvature , the unit tangent vector T and the unit normal vector 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) x x 2 + xy + e 3 xz = (b) z z sin ( x + y ) + y 2007 x = 2...
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This note was uploaded on 09/11/2008 for the course MATH 103 taught by Professor Hain during the Spring '08 term at Duke.
 Spring '08
 HAIN
 Calculus

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