Re: [微積] 如何證明lim sinx/x=1如果面積概念未定義
F
B
╮
/│ ╮ E
/ │ ╮
/ │ ╮
/__________╮
A D C
︵ __ __
A 是圓心，BC 是弧長，AB、AC 都是半徑 = 1
△ABD △BCD 都是直角三角形
∠BAD = θ
__ __ ︵
sinθ = BD < BC < BC = θ
在 B、C 點做圓弧的切線，交於 E 點，延長 AB 與 CE 交於 F
__ __ ︵
則 BE + CE > BC (外切多邊形的邊長大於圓弧)
FE > BE (直角三角形斜邊最大)
tanθ = FE + EC > BE + EC
所以 tanθ > θ > sinθ
1/cosθ > θ/sinθ > 1
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