Question

加油ㄟ

請問第一張最上面的第二小題
括號里是怎麼換成詳解那樣的？

3,求下
-100)
1
1-X100
-100
1
2x² – 5x+2
1
(2) lim
x-1
x->
1- x
(1)
H
9 9)
X
7x? +98x+99)
9
- 4950.
)
(2) lim f(x)
x->0
«).lin
lim x = 2:0=0.
x0
X
lim x² = 2.0=0.
( (2) lim|x-1-|=+
IH
2.
x+0
5
lim1=1,
x +5+
-5)
lim (-1)=-1,
(2x+3 - √x-3
-5
5
x 5
(2) lim

1-2)*+1) (2x-1)(x-2))
(2x-1)-(x+1)
=lim
-2(x-2)(x+1)(2x - 1)
-2°
(2) lim
432
x-2
x-3
x - 3
al-1
x-2
L2
-
lim
x+2
7+ 3x +9
1
99
x
2x² - 5x+2
= lim-
+-2(x-2)(x+1)(2x-1) 2 (x+1)(2x-1) 9
1
(2)原式= lim-
(1+ x + x² + ...
.. + x-100)
*+ x-1
1
= lim +x®8 +...+x-99)
xX-1
= lim(xº + 2xº? +3x® +...+97x² +98x+99)
- 100.99
=1+2+3+...+99 = = 4950. mi
2
3. 利用極限的四則運算,得--
f(x)
f (x)
(1) lim
=lim
x = lim
· lim x = 2.0=0.
x2
x1
a
9
P52
(2) lim f (x
x->0
因為
-
x →0
x=0
x x²
x →
#
(2) lim f(x)= lim f(x)
** - lim f(x). limx= 2.0=0.
x →0
(2)
x 0