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tianho 發問時間: 科學數學 · 4 年前

請優秀的大大幫我求這題極限值?

已更新項目:

我知道 When x->0, sinx/x approach to1 。

但如果我取高斯符號ㄌㄟ?

因為高斯函數在整數的地方是不連續的 (如 : 高斯函數在 1 的地方不連續)

那麼 When x->0, [sinx/x]到底是 approach to 1 還是 0 呢 ? (其中 [ ] 是高斯符號)

還是說,極限值根本就不存在?

Attachment image

2 個解答

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  • 4 年前
    最佳解答

    Refer to the photo attached

    OAB is a sector with centre O and radius 1.

    Area sector OAB =1/2 (1)x^2 =x/2

    Area of triangle OAC =tanx/2

    Area of triangle OBD =sinxcosx /2

    Area of triangle OBD < Area sector OAB <Area of triangle OAC

    sinx cosx / 2 < x/2 < tanx /2

    cosx < x /sinx < 1 / cosx

    When x->0, 1/cosx ->1, cosx ->1 ,so sinx/x approach 1 as x ->0

    Attachment image
  • 4 年前

    Area of triangle OBD < Area sector OAB <Area of triangle OAC

    sinx cosx / 2 < x/2 < tanx /2

    cosx < x /sinx < 1 / cosx

    When x->0, 1/cosx ->1, cosx ->1 ,so sinx/x approach 1 as x ->0

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