Unformatted text preview: any curve in S −→ γ ( 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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 Fall '08
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 Calculus, Derivative, order contact

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