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林貝 asked in 教育與參考考試 · 2 decades ago

[hospital法則]一題數學題目

一則數學題目,有關hospital法則

  ln(lnX^1000)

lim -----------------------

x→∞ lnX

因為∞/∞ 所以利用 hospital法則

   X

= ----------------------

  1000*lnX

還是∞/∞ 所以在利用一次 hospital法則

    1

= -----------------------

  1000*(1/x)

所以答案為∞, 不是嗎?

但答案卻是0, 我不解

1 Answer

Rating
  • 2 decades ago
    Favorite Answer

       ln(lnX^1000)

    l i m -----------------------

    x→∞  lnX

    L'hospital + chain rule

    (1/1000lnX)(1/x^1000)(1000x^999)

    => l i m------------------------------------------------

    x→∞  1/x

    整理一下

    1

    => l i m ------------------------------------------------

    x→∞  ln X

    = 0

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