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Unformatted text preview: Fall 2007 ARE211 Problem Set #12 First CompStat Problem Set Due date: Dec 04 (1) In problem 3 on your last problem set, you found the maximum and minimum distance from the origin to the ellipse x 2 1 + x 1 x 2 + x 2 2 = 3. Generalize this problem to minimize/maximize the distance from the origin to the ellipse x 2 1 + x 1 x 2 + x 2 2 = 3 and use the Envelope theorem (starting from = 1) to estimate the maximum and minimum distance from the origin to the following ellipse, x 2 1 + x 1 x 2 + 0 . 9 x 2 2 = 3 . (2) a) Prove that the expression 2 x 3 + x 5 = 17 defines x implicitly as a function of . in a neighborhood of ( , x ) = (5 , 2) b) Estimate the xvalue which corresponds to = 4 . 8 using a first order approximation. (3) Consider the equation 3 1 + 3 2 2 + 4 1 x 2 3 x 2 2 = 1. Does this equation define x as an implicit function of 1 , 2 a) in a neighborhood of ( 1 , 2 ) = (1 , 1) b) in a neighborhood of ( 1 , 2 ) = (1...
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 Fall '07
 Simon

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