TR
:
17201
TRÌNH
DÙNG CHO SV NGÀNH :
n cho các bài toán
TS
LT
TH/Xemina
BT
KT
10
8
2
0
15
10
4
1
1
1
2
1
2
1
2
1
3
1
12
8
3
1
4
1
4
2
3
1
60
42
15
3
- Anh,
-
-
-
- Sinh
1.
7
10
12
14
14
2. 2
14
2. 3.
17
2. 4.
20
2.
26
2. (Newton)
28
33
3:
34
34
34
3. 3. Newton
35
6.
54
60
60
62
64
65
Bài gi
2
1.1.
1.
, .
a.
.
Aa
(
). , nên không
. Do
a
a
.
a
( 1.1)
:
a -
a A
a
(1.3)
2.
:
a
Aa
A
Aa
(
).
.
a
( 1.4)
a
,
a
( 1.5)
a
.
Do ( 1.5) nên ( 1.2) :
A= a ( 1
a
) (1.6)
a
.
:
= 10
a
= 0,05
= 2
b
= 0,05m.
.
,
.
s
0 9,
65,807 :
65,807 = 6.10
1
+ 5.10
0
+ 8.10
-1
+ 0.10
-2
+ 7.10
-3
( 1.7)
:
1
= 6,
o
.
a
0,5 .10
s
s
,
a
>
0,5 .10
s
s
.
a
.
.
.
, v v
.
1.3. S
1.
,
.
,
5
a) 62,827;
h 62,83; (
aa '
.
a
:
aa '
( 1.8)
, .
.
:
- - a + a - A
:
.
3.
: = (
2
- 1 )
10
(1.10)
2
c
(
1.1):
Bng 1.1
2
1,4
0,0001048576
33,8
1,41
0,00013422659
10,02
1,414
.
Dx, dy,
, y, u
x
y
u
, y, u.
(1.1)
:
x
x
;
y
y
(1.12)
Ta
u
y
:
x+y
x
y
(1.13)
:
u
u
.
Bài gi
6
:
yx
.
.
3.
x
+
x
y
:
u
=
u
u
=
xy
xy
yx
=
x
x
y
y
)
= n
x
;
(1.15)
4.
/y ()
:
u
=
x
i
n
n
f
1
i
( 1.17)
u
(1.4)
: (
, theo (1.14) (1.15)
:
v
=
+ 3
d
d
= 0,05/3,7 =0,0135
Suy ra:
V
= 0,0005 + 3.0,0135 = 0,04
: V=
6
1
3
= 26,5 cm
3
.
.
.
.
2.
a) T:
A =
3
1
1
-
3
2
1
+
3
3
1
-
3
4
1
+
3
5
1
-
3
6
:
3
1
1
=
1
1
= 1,000
1
= 0
3
2
1
=
8
1
= 0,125
4
= 4.
4
10
Bài gi
8
3
5
1
=
125
1
= 0,008
5
= 0
3
6
1
=
216
125,0
2
1
3
+
037,0
3
1
3
-
016,0
4
1
1
3
+
125,0
2
1
3
+
037,0
3
1
3
+
016,0
4
1
3
+
008,0
5
1
3
+
a = 0,899 9.
4
10
:
= 0,899
9.
4
10
( 1.18 )
b) T
:
B =
3
1
1
-
3
2
1
+
3
.
,
-
3
2
1
1
1
n
3
1
n
n
B
.
n
BB
),
= 6 :
3
3
6
10.3
334
1
7
1
BB
Bài gi
9
6
B
=
6
B
+ A - 0,899
899,0899,0
6
ABBB
343
10.410.910.3899,0
B
,0
899
. Bài gi
10
1
NH
1.
.
.
.
,
.
2.
y
y
i
~
. :
y
y
i
i
( 1. 20 )
i+1
y
~
i + 1
:
y
~
i + 1
(
)
~
yy
ii
:
y
i
~
2
= q
y
i
~
1
;
y
i 2
= q
y
i 2
)
Bài gi
11
:
y
ni
~
-
y
ni
= q
n
(
y
y
1
~
=
+
yy
nini
~
=
q
n
;
1.
2.
q
1 -
q
n
q
n
,
yy
nini
~
khi n
,
: a = 21
o
o
. T
2.
:
a = 13267 ;
a
= 0,1%
b = 2,32 ;
b
= 0,7%
3.
:
a = 0,39410;
a
:
a) 2,1514; b)0,16152;
c)0,01204; d) - 0,0015281.
6.
17
1
8. : e = 1 +
!1
1
+
!2
1
+ +
!
1
n
+
10
-4
1.
a
= 0,13.10
-4
;
b
-4
; = 0,33.10
-2
d) -0,00153; = 0,19.10
-5
; = 125. 10
-2
6. a) u = 0,81;
u
= 0,27. 10
-2
;
u
= 0,33. 10
-2
b) u = 3,665;
u
= 0,7. 10
-2
;
u
= 0,20. 10
-2
7. S = 0,511.
8. e = 2,7183 0,0001.
:
f(x) = 0 (2.1)
:
.
(2.1) (2.1)
:
f() = 0 (2.2)
= 0
= .
(2.3)
:
0 = f() (2.4) 2-1
(2.1)
g(x) = h(x) (2.5)
2 (2-2)
y = g(x), y = h(x) (2.6)
= :
g() = h() (2.7)
(2.1)
.
:
2.1 -
2
(a<b) sao cho f(a) (b)
f(a).f(b) < 0 (2.8)
(x)
[a, b] [a, b]
(2.1).
.
(2.1)
[a, b]. 2-3
4. ( )
2.2
x
y
.
:
[a, b].
[a, b]
(2.1).
(x)
2.3 - [a, b] (x)
,
(x)
(a), f(b) [a, b]
(2.1)
(2.1)
y
.
:
(x). , và
2
- 1 = 0 =
3
1
thiên
x
-
x
A
B
Bài gi
17
: M = f (-
3
1
) = -
33
1
+
3
1
- 1 <0
(2.9) 2-5
[a,
b].
x
[a, b]
< b - a.
.
f(c) 0. (c)
f(a) . (c) (a)
[a, c]. (c) (a) [c,
[a, b]
, [a
2
, b
2
], [a
1
, b
1
]
[a, b]
[a
1,
, b
1
] :
b
2
- a
2
=
2
1
(b
1
- a
,
[a
n
, b
n
], [a, b] 1/2
n
[a, b] :
a
n
b
n
; b
n
- a
n
=
n
n
ab
2
)(
(2.11)
, a
n
hay b
n
.
Khi n
n
, b
n
.
.
2.
(2.9)
[1, 2].
3
2
-
2
3
- 1 > 0 (1).
[1, 3/2].
[1, 3/2],
5/4.
(5/4) < 0, (1).
[5/4, 3/2].
[5/4, 3/2],
11/8.
(11/8) > 0, (5/4).
21/16 = 1,3125 hay 43/32 = 1,34375
t1/2
5
= 1/32 = 0,03125.
Bài gi
19
5
[1,2] 2 - 1 = 1, (
(2.10)
(2.11)).
3.
= (a+b)/2, (c)
f(c)f(a)< 0
Thay b=c
Thay a=c
= b - a
e <
:
a
b
-
a
<
-
b
<
phân ly [a,b];
(2.1)
:
X = (x) (2.12)
(2.1)
0
[a,b]
n
theo quy
:
x
n
= (x
n
.
n
2.4 -
(2.13)(2.14)
1) [a,b] y
(2.1)
(2.12):
2)
n
(2.13) (2.14) [a,b]:
3) (x) :
| q <1, a<x<b (2.15)
.
:
- x
n
= () - (x
n-1
) (2.17)
.
Bài gi
(2.17)
:
- x
n
= (c)( - x
n-1
) (2.18)
= a + ( - x
n-1
) (a,b)
(2.15)
| q < 1.
(2.18) cho:
| - x
n
| = | - x
n-1
| q|- x
n-1
|
n-1
| q | - x
n-2
|
| - x
2
| q| - x
1
|
| - x
1
| q| -x
0
|
| - x
n
3) 2.4 2)
0
:
G| q < 1.
(x) > 0
0
[a,b]
( )
(a).
(2.17)
4.
:
:
a) Công thư
́
c đa
́
nh gia
́
sai sô
́
thư
́
nhâ
́
t:
:
| - x
n
|
q
q
1
| x
n
- x
n-1
| (2.23)
2.5
.
2.5.
F (x) = 0 (2.24)
[c,d]
X
[c,d]
(X) = 0
:
F (
X
) = F (
X
) - F(X)
Á
(2.18) :
F (
X
) = F' â (
X
- X)
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