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November 12th, 2008, 07:32 PM  #1 
Newbie Joined: Nov 2008 Posts: 8 Thanks: 0  finding smooth parameterization
Background: Let A(t) = (x(t),y(t)) describe a curve in the plane (parameterized by time t). Call a parameterization smooth if functions x(t) and y(t) are smooth and A'(t) (velocity) is not 0. The curve y = x for 1 <= x <= 1 is not smooth at x0 but has a parameterization A(t) = (x(t),y(t)) with x(t),y(t) smooth everywhere but A'(t) is 0 at the corner. Question: Define A: R>R... by A(t) = e^(1/x) for x > 0, and 0 elsewhere. Use A to find smooth functions x(t),y(t) that parameterize y = x for 1 <= x <= 1 I'm not sure what to do but it seems like I should define y = x for 1<= x < 0 and y = x for 0 <= x <= 1 Thanks in advance. 

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finding, parameterization, smooth 
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