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Increment Theorem for Three Variables
The following Increment Theorem has a proof like the Increment Theorem for two variables. INCREMENT THEOREM FOR THREE VARIABLES Suppose w = f(x, y, z) is smooth at (a, b, c). Let Δx, Δy, and Δz be infinitesimal. Then the increment Δw is equal to Δw = dw + ε1 Δx + ε2 Δy + ε3 Δz for some infinitesimals ε1, ε2, ε3 which depend on Δx, Δy, and Δz.
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Last Update: 2010-11-25