... ···+( 1)
n 1
x
n
n
+
( 1)
n
x
n +1
(n + 1) (1 + θx)
n +1
(1 + x)
α
=1+ αx + ···+
α(α − 1) ···(α −n +1)
n!
x
n
+
α(α − 1) ···(α −n) (1 + θx)
α−n 1
(n +1) !
x
n +1
6 0
e
−x
2
=1+ (−x
2
)+
1
2!
(−x
2
)
2
+
1
3!
(−x
2
)
3
+ ... + ···+
1
n!
f
(n)
(x
0
)∆x
n
|R
n
(∆x)| =
|f
(n +1)
(x
0
+ θ∆x)|
(n +1) !
|∆x|
n +1
= o(∆x
n
)
n
√
1+ x x
n
√
1+ x x
0
=1
n
√
1+ x ≈
n
√
1+ (...
... GIẢI TÍCH MẠNG
Trang 49
1
E F
C D A B
e
e
7
6
5
4
3
2
1
1 -1
1
-1
1
1
-1 1
1
1
1
1 1
V
ết cắt cơ bản Vết cắt giả tạo
G
... hình 4. 3 như sau:
GIẢI TÍCH MẠNG
Trang 46
nút nút
2 3
4
1
2
3
4
5
6
7
e
A =
1
-1
-1
-1
1
-1 1
-1
1 -1
Các nút
Nhánh bù cây Nhánh cây
A
b
A
t
e
-1
1
... tạo...
... v
1
, ··· ,v
k
∈ V
v
1
=
i
1
ϕ
i
1
(v
1
)e
i
1
, ··· ,v
k
=
i
k
ϕ
i
k
(v
k
)e
i
k
,
ω(v
1
, ··· ,v
k
)=ω(
i
1
ϕ
i
1
(v
1
)e
i
1
, ··· ,
i
k
ϕ
i
k
(v
k
)e
i
k
)
=
i
1
,··· ,i
k
ϕ
i
1
(v
1
) ... ϕ
2
)(v
1
,v
2
)=ϕ
1
(v
1
)ϕ
2
(v
2
) − ϕ
2
(v
1
)ϕ
1
(v
2
) = det
ϕ
1
(v
1
) ϕ
1
(v
2
)
ϕ
2
(v
1
) ϕ
2
(v
2
)
R
2
ϕ(v
1
),ϕ(v
2
) ϕ =(ϕ
1...
... n
k
=[x
k
]
1
n
k
+1
≤
1
x
k
≤
1
n
k
1+
1
n
k
+1
n
k
≤
1+
1
x
k
x
k
≤
1+
1
n
k
n
k
+1
lim
k→∞
1+
1
k
k
= e lim
x→+∞
(1 +
1
x
)
x
= e
lim
x→−∞
(1+
1
x
)
x
= lim
y→+∞
(1
1
y
)
−y
= ... +1)
(
3
√
x
2
+
3
√
x +1)
(
√
x +1)
(
√
x +1)
= lim
x 1
x − 1
x − 1
(
√
x +1)
(
3
√
x
2
+
3
√
x +1)
= lim
x 1
√
x +1
3
√
x
2
+
3
√
x +1)
=
√
1+ 1
3...
... a
0
−
a
1
10
<
1
10
a
2
∈{0, 1, ··· , 9}
a
2
10
2
≤ x − a
0
−
a
1
10
<
a
2
+1
10
2
n 0 ≤ x − a
0
−
a
1
10
−···−
a
n
10
n
<
1
10
n
a
n +1
= [10
n +1
(x − a
0
−
a
1
10
−···−
a
n
10
n
)] a
n +1
∈{0, ... +2)− (n +1)
√
n +2+
√
n +1
= lim
n→∞
√
n
√
n(
1+
2
n
+
1+
1
n
)
= lim
n→∞
1
1+
2
n
+
1+
1
n
=
1
(lim
1+
2
n
+ lim
1+
1
n
)
=
1...
... j
i∈I
L
i
1+ x + x
2
+ x
3
+ ··· =
1
1 − x
1
x
+
1
x
2
+
1
x
3
+ ··· =
1
x (1 − 1/ x)
=
1
x − 1
···+
1
x
3
+
1
x
2
+
1
x
+1+ x + x
2
+ x
3
+ ··· =0 x =0, 1
∞
k =1
x
k
k
2
∞
k=0
k!x
k
∞
k=0
k
k +1
(x ... +1
(x 1)
k
∞
k=2
(x +2)
k
ln k
∞
k =1
1
2
k
k
x
k
∞
k =1
( 1)
k
k
x
2k +1
∞
k =1
1
k
x
2
2k
∞
k=0
x
k
∞
k=0
(k +1) x
k
∞
k=0
x
k +...
... (0, 0)
(1, 1) D
1
=6> 0,D
2
=27> 0 Hf (1, 1) > 0 f (1, 1)
1
0
(φ
1
(t), ··· ,φ
m
(t))dt =(
1
0
φ
1
, ··· ,
1
0
φ
m
)
f : U → R
m
U Df(x)=0, ∀x ∈ U
f ≡
f : U → R
n
U ⊂ R
n
C
1
K
U ... b) θ ∈ (0, 1)
g(x+h)=g(x)+
1
1!
g
(x)h+
1
2!
g
(x)h
2
+···+
1
(k 1) !
g
(k 1)
(x)h
k 1
+
1
k!
g
k
(x+θh)h
k
.
f : R
n
→ R
g(t)=f (x + th),t∈ [0, 1] .
∇ =(D
1...
... →∞.
∞
k=0
x
k
f(x)=
1
1 − x
[ 1, 1) 0 ≤ r< ;1
[−r, r]
S
k
(x) =1+ x + ···+ x
k
=
1 − x
k +1
1 − x
[−r, r]
sup
|x|≤r
|S
k
(x) − f(x)| =sup
|x|≤r
x
k +1
1 − x
=
r
k +1
1 − r
→ 0, k →∞.
f ( 1, 1)
2
n
,n
p
, ... y)=(x + y)sin
1
x
sin
1
y
. a
12
,a
21
a =0
f(x, y)=
x
2
− y
2
x
2
+ y
. a
12
=0,a
21
=1 a
f(x, y)=
xy
x
2
+ y
2
. a
12
= a
21
=0 a
f(x...