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Unformatted text preview: REVIEW OF THE CHAPTER 12 Problem 1. Find the total differential of the function f ( x, y ) = xye x y at the point (0 , 1) . Solution. The total differential of the function z = f ( x, y ) given by formula dz = f x ( x, y ) dx + f y ( x, y ) dy. For our function we have f x ( x, y ) = ye x y + xe x y , f y ( x, y ) = xe x y- x 2 y e x y Next we need to find the values of the partial derivatives at the point (0 , 1) . f x (0 , 1) = 1 f y (0 , 1) = 0 . Hence dz = dx. Problem 2. The surface is given by equation F ( x, y, z ) = x 2 + y 2- z 2 = 0 . Find equations of a normal line and a tangent plane to this surface at the point P = (1 , , 1) . Solution. The equation of the tangent plane to the surface F ( x, y, z ) = 0 at the point P = ( x , y , z ) is given by formula F x ( x , y , z )( x- x )+ F y ( x , y , z )( y- y )+ F z ( x , y , z )( z- z ) = 0 . (1) And the equation of the normal line to the surface F ( x, y, z ) = 0 at the point P = ( x , y , z ) is given by formula x y z = x y z +...
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This note was uploaded on 11/14/2010 for the course CHEM 232435545 taught by Professor Aa during the Spring '10 term at University of Illinois, Urbana Champaign.
- Spring '10