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Check for understanding When zooming for the derivative at a point on a linear field -- what do you expect to see? At every point the derivative of a linear object is the same linear object! Here the lens correctly shows a copy of the harmonic oscillator: By linearity L(x0 + Dx) - L(x0) = L(Dx). Recall zooming in on the graph of a linear function of a single variable L(x0 + Dx) - L(x0) = L(Dx) = m Dx.
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