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Unformatted text preview: u and v . c) (3) Find xw x + yw y in case w = v 5 . Problem 5. a) (10) Find the Lagrange multiplier equations for the point of the surface x 4 + y 4 + z 4 + xy + yz + zx = 6 at which x is largest. (Do not solve.) b) (5) Given that x is largest at the point ( x , y , z ), ±nd the equation for the tangent plane to the surface at that point. Problem 6. Suppose that x 2 + y 3-z 4 = 1 and z 3 + zx + xy = 3. a) (8) Take the total di³erential of each of these equations. b) (7) The two surfaces in part (a) intersect in a curve along which y is a function of x . Find dy/dx at ( x, y, z ) = (1 , 1 , 1)....
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This note was uploaded on 04/18/2008 for the course 18 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
- Fall '08