SÁNG KIẾN KINH NGHIỆM
ĐỀ TÀI:
"GI H SINH N ỆN K N NG GI I H NG
NH H NG NH "
Trang 2
I N :
- -
m
k
Trong
h
- n
-
-
II S N:
chung
,
Trang 3
sinh
III S H I N: B
: AB, A B A B nêu n
, khi
-
IV N I NG A
1) g f(x) g(x) : 2x 1 3x 1
ta ch 3x 1 0 3 1 x
9
4 0
9
4 ,
0 3 1
0 4 9
3
1 )
1 3 ( 1
2
0 1 3
2
x x
x x
x
x x
x
x
pt
Trang 4
) ( ) ( 0 ) ( ) ( ) ( 2 x g x f x g x g x f f(x) 0) t 2x 1 x 4 1 x 1 2x
2 1 4 x (*) pt x 4 1 2x 1 x x 4 1 2x 2 ( 1 2x)( 1 x) 1 x 0 0 7 2 2 1 ) 1 )( 2 1 ( ) 1 2 ( 0 1 2 ) 1 )( 2 1 ( 1 2 2 2 x x x x x x x x x x x
: 1 x
p
f(x) g(x) : ) ( ) ( 0 ) ( 0 ) ( ) ( ) ( 2 x g x f x f x g x g x f 3: 2x2 6x 1 x 2 (1)
2 2
2
) 2 ( 1 6 2
0 1 6 2
0 2 )
1
(
x x
x
x x x
0 3 2
2
7 3 2
7 3
2
2
x x
Vx x
x
3 1
2
7 3 2
7 3
2
x
Vx x
x
3 2
7
3
f(x) g(x) :
) ( ) (
0 ) (
0 ) (
0 ) (
)
(
)
(
2
x g x f
x g
x g
x f x
g
x
f
Trang 54: bpt:
3
7 3 3
) 16 (
2 2
x
x x
x
x - 2004)
x 4 bpt 2 2 2 2 2 ) 2 10 ( ) 16 ( 2 0 2 10 0 2 10 0 16 2 10 ) 16 ( 2 7 3 ) 16 ( 2 x x x x x x x x x x 34 10 5 34 10 5 x x x 5: 2x 6x2 1 x 1
2 2 2 2 2 2 2 ) 1 ( 1 6 1 1 1 6 1 ) 1 ( 1 6 2 0 1 x x x x x x x x x x pt 0 , 2 0 4 1 2 4 x x x x x : x(x 1 ) x(x 2 ) 2 x2 (*)
0 1 2 x x x Pt 2x2x 2 x2(x 1 )(x 2 ) 4x2 2 x2(x2x 2 ) x( 2x 1 ) 2 2 2 2 ) 1 2 ( ) 2 ( 4 x x x x x
8 9 0 0 9 8 2 x x x x
:
1)
*
* x 1 pt x 1 x 2 2 x 2 x2x 2 2x 1 8 9 1 4 4 8 4 4 2 2 x x x x x
* x 2 pt x( 1 x) x( x 2 ) 2 ( x)( x)
Trang 69 1
2 2 2
2 2
1 2
8 9
k ab a b!
a,b 0 a,b 0 ab a b.
: 3 3 3
3 2 2
1
pt 2x 3 3 3 (x 1 )(x 2 (3 x 1 3 x 2 ) 2x 3 (*)
0 ) 3 2 )(
2 )(
1 (
3 2 2 1
3
3 3
3
x x
x
x x
x
2
3
; 2
;
1
:
a
?
! 0 ) 3 2 )(
2 )(
1 ( 3 2 ) 2 1
( 2 )(
1 (
3
3
2x 3 x x 3 x 3 x x 3 x x x
pt sau:
0 1
1 1 ) 1 1
( 1 3 2 1 1
3 x x x x x x x
b 3 3 3
c b
a t
) ( 3 )
(ab 3 a3b3 ab ab t
0
33
3 3 3
c b a b a
c b
8: a) x2 x 7 7(1)
b)
5
3 2
3 1
4 x
x
a) pt x2 (x 7 ) (x x 7 ) 0 (x x 7 )(x x 7 1 ) 0
1 7
7
x x
x x
Trang 7
2
2
29
1
x
x x 2
2
29
1
b) pt 5 ( 4x 1 3x 2 ) ( 4x 1 ) ( 3x 2 )
) 2 3 1 4 ).(
2 3 1 4 ( ) 2 3 1
4
(
0 2 3 1
4
0 2 3 1
4
x x
x
x x
: *
y x 7
7
7
2 2
y x
x
y (yx)(yx 1 ) 0
* D : x2 xa a
5
2 2
2 3
) 2 ( 3 3 1 4
) 2 ( 4 5
2 2
2 3 3 1
x
x x
x x
x x
(*) 5
1 ) 2 2 3 )(
3 1
4
(
1 1 4 2 3
2
x x
x x
x
(do )
3
2
x
9:
) 1
1
2
x
(1) b) (x2 3x) 2x2 3x 2 0 (2)
x 1
0 1 x 1 0 Nhân l
8 3
1 4
) 1 1
( 4 )
1 1 (
)
1
1
(
) 1
1
2 2
2 2
x x
x x
x x x
x x
T [ 1 ; 8 )
Trang 8
TH 1: 2x2 3x 2 0 x 2 V
2
1
x , k
TH 2: BPT 3 2 1 3 0 2 2 1 0 3 0 2 3 2 2 2 x Vx Vx x Vx x x x x x o ] { } [ 3 ; )
2 1 ; ( T :
g
c
: :
1 3 2x2mx x
(*) 0 4 ) 2 ( 1 2 x m x x pt P
0 2 8 4 2 ; 0 2 8 4 2 2 2 2 1 m m m x m m m x (*) 1
2 8 4 ) 4 ( 4 8 4 4 1 2 2 2 2 m m m m m m m m x m 2
B
1: F(n f(x) 0, t n f(x)
) 0 t r t x.
af(x) b f(x) c 0
a) x2 x2 11 31 b) (x 5 )( 2 x) 3 x2 3x
Trang 9
a) t x2 11 ,t 0 K
5 6
11 6
0
2 t t x x
t
b) ptx2 3x 3 x2 3x 10 0 t x2 3x, t 0
2
109 3
0 25 3 5
3 5
0
10
2
x x
x x
x t
t
t
m x2 2x 2m 5 2xx2 m2.
t 5 2xx2 6 (x 1 ) 2 t [ 0 ; 6 ] 2 2
5
2x t
x
t2 2mtm2 5 0 (*) tm 5
(*) t [ 0 ; 6 ], hay:
5 6 5
5 6 5
6 5
0
6 5
0
m
m m
m
m[ f(x) g(x ] 2n f(x).g(x) n[f(x) g(x)] p 0
t f(x) g(x)
: 3 x 6 x m ( 3 x)( 6 x)
m 3
b) m
t 3 x 6 x t2 9 2 ( 3 x)( 6 x)(*)
2 ( 3 x)( 6 x) 9 3 t 3 2
t m t t 2t 9 2m
2
9 2
2
m 3 t2 2t 3 0 t 3 (*)
6
3 0
) 6
)(
3
(
x
x x
b) ( 1 ) t [ 3 ; 3 2 ]
Trang 10f(t) t2 2t 9 t [ 3 ; 3 2 ] f (t)
] 2 3
; 3 [ , 2 6 9 ) 2 3 ( ) ( )
3
(
2
9 2 6 2 6 9 2 6 ] 2 3
; 3 [
t
m ; 3 ]
2
9 2 6
[
:
Y f(x) k
D kY.
: 2x 3 x 1 3x 2 ( 2x 3 )(x 1 ) 16
x 1
t 2x 3 x 1 ,t 0 t2 3x 2 ( 2x 3 )(x 1 ) 4 (*)
tt2 20 t2t 20 0 t 5
Thay t 5 21 3x 2 2x2 5x 3
12 20 8
9 126
441
7 1
2 2
x x
x x
x
0 429 146
7 1
2
x x
x
3
x
F(n f(x) ,n g(x ) 0 f (x) k
:
TH 1: g(x) 0
TH 2: g(x) 0 g k (x) n
x g
x f t
) (
) (
0
)
(
1 t
F k
: a.f(x) b.g(x) c. f(x)g(x) 0
: : 5 x3 1 2 (x2 2 )
x 1 5 (x 1 )(x2x 1 ) 2 (x2x 1 ) 2 (x 1 )
0 2 1
1 5
1
1
x x
x x
x
x
(Do x2 x 1 0 , x).
Trang 11, 0
1
1
x x
x
t , t
2 1
2 0
2 5
2 2
t
t t
1
1
2 2 2
x x
x
*
2
37 5 0
3 5 4
1 1
1 2
2
x x
x
t
: Trong nh
: x2 2x 2x 1 3x2 4x 1
3 1 4 3 1 2 ,
x
0
3 2 2 2 2
2
5 1 2 2
5
1 2
2
5
1
x
: m :
4 2
1 2
1 1
3 x m x x A - 2007)
x 1
*x 1 m 0
* x 1 , 4 2
1
1
1 1
1
3 4 4
x
x m x
x
1
2 1 1
1
4
4
x x
x
m t t t
m
t 2 3 2
(*) t ( 0 ; 1 )
3 2 1 , ( 0 ; 1 ) (*)
3
1 2
3
1 1
1 3
1
3
1
1
Trang 12
i l
a.f(x) g(x). f(x) h(x) 0 t f (x)
: at2g(x)th(x) 0
8: 2 ( 1 x) x2 2x 1 x2 2x 1 t x2 2x 1 t: t2 2 ( 1 x)t 4x 0
2
) 1 ( ' x t 2 ,t 2x. *t 2 x2 2x 1 2 x2 2x 5 0 x 1 6 * 0 1 2 3 0 2 1 2 2 2 2 x x x x x x x t
x 1 6 :
9: 2 2 2 1 1 x x
1 1 x 2 2 1 x a
x 1 x cost,t [ 0 ; ]
2
1 sin 0 1 sin sin
2 cos
2 cos
1
1 2t 2t 2t t t (do sint 0 ).
Trang 13
2
3 sin
1 cos 2
x
:
u(x) a ]
2
; 2 [ , sin )
(
t t a x
u u(x) acost,t [ 0 ; ]
u(x) [ 0 ;a] ].
2
; 0 [ , sin )
( 2
t t a x u
: x3 ( 1 x2)3 x 2 ( 1 x2)
x 1
x cost,t [ 0 ; ]
t t t
t t
t t
t t
t sin 2 cos sin (sin cos )( 1 sin cos ) 2 sin cos
0 2 3 2 2
1 2 ) 2
1
1
2 2
2 0
) 1 2 2 )(
2
u u u u V u 2 1
2
2 4
cos 4
1 ) 4 cos(
2
x t
t u
*
) 2 1 ( 1
2 1 2
1 1
2
1
x x
x x
x u
2
2 2 2 1 0
2 1 ) 2 1
(
2 1
x x
x
11: xx x 1 x
3
2
0 x 1
Trang 14
2 2 2 2
2 2
2 1 ) ( 9
4 3
4 1 1
3
2
1
)
1
( x x x x xx xx xx
VN
Vx x x
x
x x x
x x x x
x x
2 3
0 0
3 2
0 3
)
(
2 2
2 2
2
2
x x x 1 x
2 2 2 1 1 x x x x t x 1 x
2 1 2 2 x t x
2 1 0 2 3 3 1 1 2 2 t t t t t t
1 0 0 2 2 1 1 1 2 x x VN x x x x x x x 1 x t
(*)
x 2 1 x2 x 1 x 1
sin2 cos2 1
sin , 0;2 2 t t x x 0 ; 1)
0 ) 3 sin 2 ( sin 1 )(
sin 1 ( ) sin 1 ((
3 cos sin cos
.
sin
3
2
1 t t t t t t t t
0
1 0
) 8 sin 6 sin 4 ( sin
1 sin
1 ) sin 2 3 ( sin
1
3
1 1
sin
2
x
x t
t t
x t
t t
x t
Trang 15
,
VI KẾ NGHI N
sinh
-
10 tôi
sinh ,
thêm m Riêng
t p Ngoài ra,
và C ;
II KẾ N
môn T
Tr
VIII KIẾN NGH
tôi :
-
-
u k