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Unformatted text preview: i j ? (c) Along what curve through the point (2, -1) should the ant move in order to continue to experience max. rate of cooling? 5) If sin x t s = and cos y t s = . Assuming ( , ) f x y is differentiable: (a) Find 2 ( , ) f x y s t (b) Find 2 2 ( , ) f x y s . 6) Show that the equations 2 2 3 3 2 2 1 xy zu v x z y uv xu yu xyz + + = +-= +-= can be solved for x, y and z as functions of u and v near point P where (x,y,z,u,v) = (1,1,1,1,1) and find v y u at (u,v) = (1,1) . 7) Find the maximum and minimum values of 2 2 ( , ) 1 x f x y x y = + + . 8) Use Lagrange multipliers to find the shortest distance from the origin to the surface 2 2 xyz = . 9) Find the volume of the solid bounded by the plane z = 0 and the paraboloid 2 2 1 z x y = --....
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- Spring '08