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Answers for “$f(x)\Delta x$ 的几何解释是什么?”

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The corner term represents the product of two small changes, ΔfΔg\Delta f \Delta g. Because the functions are differentiable, both Δf\Delta f and Δg\Delta g are of order hh (proportional to the input increment).

Conditions: Functions ff and gg are differentiable at the point.; The input increment hh approaches zero.; The geometric model assumes a rectangle with sides f(x)f(x) and g(x)g(x).