Hung Fung book 2 (Theorem3-3)

👨🏻‍🏫 學術台數學

Atheist

2011-12-01 5:51 am

If lim(x->a)f(x) exists, then f(x) is bounded at the points near x=a. (The result may not hold at the point x=a.)

What does that mean???????????????????????????????
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更新1:

This theorem is rubbish, right?

回答 (1)

myisland8132

2011-12-01 7:18 am

✔ 最佳答案

若果lim(x->a)f(x) 存在, 則 f(x) 在x = a 附近有界

這是很明顯的。因為lim(x->a)f(x)存在表示0 < | x − a | < δ 蘊含 | f(x) − L | < ε

因此L - ε < f(x) < L + ε

👍 0 👎 0

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