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Unformatted text preview: dicular. (c) Three lines that are mutually skewed to each other. (d) Three nonintersecting planes. 4. (10 pts)Find lim ( x,y ) → (0 , 0) x 5 + y 5 x 4 + 2 x 2 y 2 + y 4 if it exists and justify your answer. 5. (10 pts) Find lim ( x,y ) → (0 , 0) x 2 x 2 + y 2 if it exists 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 (2 , 3 , 4) the curvature κ , 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 , , 3). 8. (10 pts) Compute the following partial derivatives. (a) ∂ ∂x ‡ x 2 + xy + ln (3 xz ) · = (b) ∂ 2 ∂x∂y ‡ x 2 + cos( x ) sin(8 y ) + x z y · = 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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