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Unformatted text preview: any curve in S ( t ) = p ( r ( t ) ,s ( t )) = ( x ( r ( t ) ,s ( t )) ,y ( r ( t ) ,s ( t )) ,z ( r ( t ) ,s ( t ))) the velocity vector v (0) = p r dr dt + p s ds dt lies in the plane parametrized by T p . It is also a straightforward argument to show that this parametrization of the tangent plane has frst order contact with p ( r,s ) at ( r,s ) = ( r ,s ), in the sense that v v v p ( r + r,s + s ) T ( r ,s ) p ( r + r,s + s ) v v v = o ( b ( r, s ) b ) as ( r, s ) ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus

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