1. Determine whether the following function is differentiable at x = 0.
f(x) =
{x^2, if x is rational,
{0, if x is irrational.
2.Determine whether the following function is differentiable at x = 0.
f(x) =
{Δx, if x is rational,
{0, if x is irrational.
Differentiability
2013-10-26 6:48 am
回答 (2)
2013-10-26 8:27 am
✔ 最佳答案
請參考看看，第二題也可以造兩串數列，一串是有理數量收斂到0，一串用無理數列收斂到0，然後兩個的極不相等，所以不收f'(x)的極限不收斂，也就不可微。圖片參考：http://imgcld.yimg.com/8/n/AA00645012/o/20131026002333.jpg
2013-10-26 01:24:09 補充：
哈哈哈，對耶，用錯了 qq
2013-10-26 01:25:15 補充：
on real line R^c = empty set
orz
2013-10-26 08:57:14 補充：
如 Masterijk大大的提醒，請將 R改成 Q，晚上寫數學，頭暈暈 不好意思啊。
謝謝 Masterijk大。
2013-10-26 8:51 am
Wan 大~
應該用 Q 指 rational numbers.
應該用 Q 指 rational numbers.
收錄日期: 2021-04-16 16:16:16
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https://hk.answers.yahoo.com/question/index?qid=20131025000051KK00235