Engineering Calculus Notes 343

Engineering Calculus Notes 343 - x,y,z ) , (0 , , 0)) 2 = x...

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3.6. EXTREMA 331 closest to the origin. We characterize the surface as L ( g, 1), where g ( x,y,z ) = xyz −→ g ( x,y,z ) = ( yz,xz,xy ) . As is usual in distance-optimizing problems, it is easier to work with the square of the distance; this is minimized at the same place(s) as the distance, so we take f ( x,y,z ) = dist((
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Unformatted text preview: x,y,z ) , (0 , , 0)) 2 = x 2 + y 2 + z 2 f ( x,y,z ) = (2 x, 2 y, 2 z ) . (See Figure 3.27 ) b x y z Figure 3.26: Level Curves of f ( x,y,z ) = x 2 + y 2 + z 2 on the surface xyz = 1 The Lagrange Multiplier Equation f = g...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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