Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Lakers asked in 教育與參考考試 · 1 decade ago

如何證明這個limit等式?

當x趨近於0的時候 sinx/ x 則會趨近於1??

前提是x必須以radian表示 (抱歉我不知道中文= =)

1 radian= 180度

這樣如何證明???

Update:

啊啊~~眼花了 抱歉上面打錯= = 謝謝回答啊~~~XD

Update 2:

抱歉我數學很爛 為什麼sinx<=x<=tanx 解釋一下~~~感謝!!

1 Answer

Rating
  • 1 decade ago
    Favorite Answer

    首先回答您, radian 的中文名稱是 "弳度"

    其次再說明, 1 rad ≠ 180°, 您的觀念有誤

    1π = 180°

    1 = 180°/π = 180°/3.14159 ≒ 57.30°

    而 1, 也就是所謂的 1 radian, 角度大約是 57.30°

    ok, 現在回歸到您的問題來

    您的問題可以用夾擠定理來証明

    sinx ≤ x ≤ tanx

    1 ≤ x/sinx ≤ 1/cosx (兩邊取 lim(x→0))

    1 ≤ lim(x→0) x/sinx ≤ lim(x→0) 1/cosx = 1

    ⇒ lim(x→0) x/sinx = 1

    ⇒ lim(x→0) sinx/x = 1 #得証

    http://tw.myblog.yahoo.com/jw!JCVbjQyaBRbXTWOakinc...

    2008-09-24 21:53:04 補充:

    您所需要的証明, 可直接在前往部落格閱覽

    Source(s): 思瑜的部落格
Still have questions? Get your answers by asking now.