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Unformatted text preview: function of the form p ( t ) = ( x ( t ) ,y ( t ) ,z ( t )) = ( x ( t )) + ( y ( t )) + ( z ( t )) k with non-vanishing velocity v ( t ) := V p ( t ) = ( x ( t ) ,y ( t ) ,z ( t )) = ( x ( t )) + ( y ( t )) + ( z ( t )) k n = (or equivalently, non-zero speed) ( x ( t )) 2 + ( y ( t )) 2 + ( z ( t )) 2 n = 0 . We can no longer talk about such a curve as the graph of a function, but we can get a kind of analogue of the second statement in Proposition 2.4.7 which can play a similar role: Remark 2.4.8. If p ( t ) is a regular vector-valued function with values in R 3 , then locally its projections onto two of the three coordinate planes are graphs: more precisely, for each parameter value t = t at least one of the...
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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