→ ytyt5239 :謝謝了，你好棒~ 12/08 16:42
※ 引述《ytyt5239 (ytyt)》之銘言：
: 1.use the mean value theorem to prove the inequality
: ｜sin a - sin b｜ <= ｜a-b｜ for all a and b
: 是要分三個case嗎?? a>b a=b a<b
mean value theorem:
if f(x) is continued in [a,b]
f(b)-f(a)=f'(c）(b-a)
a<c<b
let f(x)=sinx
=> sina-sinb=cosc(a-b)
=> |sina-sinb|=|cosc||a-b|
=> |cosc|<=1
so |sina-sinb|<=|a-b|
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