推 JimCroce:謝謝STYLE520大大教導 219.91.104.243 07/26
※ 引述《JimCroce (我要下五子棋 N )》之銘言：
: Suppose f is function with the property that
: l f(x) l 小於等於 x^2 for all x. Show that f is differentiable at 0.
: ^^^^^^^^^
: 絕對值f(x)
: 請問怎麼show在0不可微? 謝謝回答!
證明:
|f(0)| <= 0^2 = 0 => f(0) = 0
|f(x)| < x^2 ==> -x^2 < f(x) < x^2
f(x) - f(0) f(x)
-|x| < ----------- = ----- < |x|
x - 0 x
lim -|x| = lim |x| = 0
x->0 x->0
f(x) - f(0)
由三明治定理 f'(0) = lim ----------- = 0
x->0 x - 0
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※ 編輯: style520 來自: 140.112.250.72 (07/26 19:12)