Re: [微積] 如何證明lim sinx/x=1如果面積概念未定義
If the integration formula for arc length is allowed to use:
Let y=√(1-x^2), then 1+y'^2=1/(1-x^2), so, for 0<θ<Pi/2,
1
θ=∫ dx/√(1-x^2) .
cosθ
Since x/√(1-x^2) <= 1/√(1-x^2) <= 1/ x^2√(1-x^2) when x in (0,1),
after taking integration from cosθ to 1,
we get sinθ<= θ <= tan θ.
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