匿名使用者
匿名使用者 發問時間: 科學數學 · 5 年前

Calculus Chapter 6 Differential Equations(1)?

各位高手:

請問第99題要如何證明?

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1 個解答

評分
  • 5 年前
    最佳解答

    Consider an integral curve y = f(x) with gradient q(k) - p(k)f(k) at x = k.

    The tangent at (k, f(k)) has equation y - f(k) = (q(k) - p(k)f(k))(x - k).

    When x = 1/p(k) + k, y = f(k) + (q(k) - p(k)f(k))/p(k) = q(k)/p(k),

    so every such tangent passes through the point (1/p(k) + k, q(k)/p(k)).

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