Question

粉猩猩

（大一微積分）
請問這題這樣寫正確嗎？背流程寫的😅，圖一為需用到的定義
正確的話，想問紅色圈圈的1是怎麼來的？

DEFINITION Let f be a function defined on some open interval that con-
tains the number a, except possibly at a itself. Then we say that the limit of
f(x) as x approaches a is L, and we write
lim f(x) = L
x→a
if for every number &> 0 there is a corresponding number 8 >0 such that
| ƒ(x) − L| < ɛ
if 0 < x-a <8 then

33-44 Prove the statement using the e, 8 definition of a limit.
44. lim (x² + x - 4) = 8 [Hint: If|x - 3| < 1, what can
x →3
you say about x + 4 [?]
Let & so be given arbitrarily.
(x+ X- 4) - 8 |=|x+4||-3|
if x-3|<1 then -/<^-3 < 1
6<x+4 < 8
→ 8
|x+4/<
choose d = min {D, & }
if 0< x-3|<d then (x²+x-4) - 8
二 | x+4|| 人- 3 |
<88=E
..
Lim (x² + x + 4) = 8 #
X-3

微積分 極限 calculus limit