Question

wimdot

想請問學霸們畫線的地方是什麼意思？（看得懂英文，不過他想表達的我就不懂啦~QQ)-大一入門微積分

Precise meaning of limit
x->a
For each € > 0 there is a 8 >0 such that 0 <|x - al<8 = \|(x) – Ll<ɛ
1.Prove that lim (3x – 7)= 5
x 4
Prove :
Preliminary Analysis : Let ε be any positive number. We must produce a 8 >0 such that
0<fx - 4<= |(3x - 7)- 51 <
digital do
consider the inequality on the right
|(3x – 7)-5/<ε = 3x - 12/<€ 3(x-4)<ɛ
how blu 4< = |-
- 131x - 4 <E (x-4 < 2 3
domen. szondo otworo
Now we see how to choose 8, namely, 8 = Of course, any smaller 8 would work
Toolmo
Formal Proof : Let & > 0 be given. Choose 8 = . Then 0 < x - 4 <& implies

Answer 1

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Ryan

意思是從結果來看只要delta=epsilon/3就一定保證這個函數在x以在該區間內趨近於4的時候會等於5，而delta若比epsilon/3更小就表示x趨近於4仍在以上區間內，因此該函數的極限值當然還會是5。

wimdot

喔喔原來如此~