[微積] 極限定義證明一題
因為是自學的，那麼晚沒老師問，就來版上發問了！（其實剩三十多天就要考跟這個無
關的試，真是罪孽）
就是一題利用ε－δ def. 的證明，看看自己有沒有對
lim x^2 + 2 = 3
x->1
| x^2 - 1 | < ε
| (x+1)(x-1) | < ε
(x+1)| (x-1) | < ε
故若 3| (x-1) | < ε , 可滿足上式
| (x-1) | < (1/3)ε
那麼讓 δ= (1/3)ε
0 < | (x-1) | < δ(=(1/3)ε)
0 < | (x-1) | < (1/3)ε
0 < 3| (x-1) | < ε
推回 | x^2 - 1 | < ε
感覺錯了，不太理解δ、ε的關係如何取到最好
另外求解一題：
lim cosx = 1
x->0
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 219.85.40.200
→
04/17 01:54, , 1F
04/17 01:54, 1F
→
04/17 01:57, , 2F
04/17 01:57, 2F
→
04/17 01:58, , 3F
04/17 01:58, 3F
→
04/17 02:00, , 4F
04/17 02:00, 4F
→
04/17 02:01, , 5F
04/17 02:01, 5F
→
04/17 02:05, , 6F
04/17 02:05, 6F
→
04/17 02:07, , 7F
04/17 02:07, 7F
→
04/17 02:09, , 8F
04/17 02:09, 8F
→
04/17 02:10, , 9F
04/17 02:10, 9F