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Unformatted text preview: x = y = . 2 and z can vary by at most z = . 1. The best estimate of this is the diFerential: f ( x,y,z ) = xyz f x ( x,y,z ) = yz f y ( x,y,z ) = xz f z ( x,y,z ) = xy and at our point f x (5 , 10 , 2) = 20 f y (5 , 10 , 2) = 10 f z (5 , 10 , 2) = 50 so the diFerential is d (5 , 10 , 2) f ( x, y, z ) = 20 x + 10 y + 50 z which is at most (20)(0 . 2) + (10)(0 . 2) + (50)(0 . 1) = 4 + 2 + 5 = 11 . We conclude that the gure of 100 cubic feet is correct to within 11 cubic feet. Exercises for 3.3 Practice problems:...
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 Fall '08
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 Calculus

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