|
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
27
3.
î
í
ì
¹
³
Û
³
0
)
(
0
)
(
)
(
0
)
(
)
(
x
Q
x
Q
x
P
x
Q
x
P
. 4.
î
í
ì
¹
£
Û
£
.
0
)
(
0
)
(
)
(
0
)
(
)
(
x
Q
x
Q
x
P
x
Q
x
P
.
Modulli tenglamalar
Moduli tenglamalar quyidagicha ekvivalent almashtirish bilan
yechiladi:
1.
( )
( )
( )
0
f x
f x
f x
=
Û
³ ; 2.
( )
( )
( )
0
f x
f x
f x
= -
Û
£
;
3.
( )
( ),
( )
0,
( )
( )
( )
( ),
( )
0;
F x
f x
agar F x
F x
f x
F x
f x
agar F x
=
>
é
=
Û ê
= -
<
ë
4.
2
2
( )
( )
( )
( )
f x
g x
f
x
g
x
=
Û
=
; 5.
2
2
( )
(
0)
( )
f x
a
a
f
x
a
=
>
Û
=
;
6.
( ,
)
0,
0,
( ,
)
0
( ,
)
0,
0;
F x x
a
agar x
a
F x x
a
F x
x
a
agar x
a
-
=
- ³
é
-
= Û ê
- +
=
- <
ë
7.
( )
( ),
( )
( )
( )
( );
f x
g x
f x
g x
f x
g x
=
é
=
Û ê
= -
ë
8.
( ) ( ), 0,
(
)
( )
(
)
( ), 0;
f x
g x
agar x
f x
g x
f
x
g x
agar x
=
³
é
=
Û ê - =
<
ë
9.
( )
( )
(
0)
( )
f x
a
f x
a
a
f x
a
=
é
=
>
Û ê
= -
ë
; 10.
( )
(
0)
f x
a
a
=
<
Û Æ
.
Modulli tengsizliklar
Moduli tengsizliklar quyidagicha ekvivalent almashtirish bilan
yechiladi:
1.
( )
(
0)
( )
f x
a
a
a
f x
a
<
> Û- <
< ;
2.
2
2
( )
(
0)
( )
f x
a
a
f
x
a
>
> Û
>
yoki
( )
,
( )
(
0)
0
;
( )
;
f x
a
f x
a
a
agar a
x
R
f x
a
>
é
>
> Û
< Þ Î
ê
< -
ë
3.
2
2
( )
( )
( )
( )
f x
x
f
x
x
j
j
<
Û
<
;
4.
( ) ( ), 0,
(
)
( )
(
)
( ), 0;
f x
g x
agar x
f x
g x
f
x
g x
agar x
<
³
é
<
Û ê
- <
<
ë
5.
( )
( ),
( )
( )
( )
0
;
( )
( );
f x
g x
f x
g x
agar g x
x
f x
g x
<
ì
<
Û
£ Þ ÎÆ
í-
<
î
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
28
6.
( ) ( ),
( ) ( ) 0,
( )
( )
( )
( )
(
)
( ) 0;
f x
g x
f x
g x
agar x
f x
g x
yoki
f x
g x
f
x
g x
agar x
é
>
é
>
³
>
Û ê
ê
< -
-
>
<
ê
ê
ë
ë
7.
( )
( )
2
2
( )
( )
0 0
( )
0 0 ; 0,
n
n
n
a f
x b f x
c
f x
y
ay
by c
y
n N
+
+ ³ £ Þ
= Þ
+ + ³ £
³
Î
Irrasional tenglama.
Irrasional tenglamalarni umumiy holda quyidagicha
ekvivalent almashtirish yordamida yechish mumkin
(
)
n
N
Î
:
1.
2
2
( )
0,
( )
( )
( )
0,
( )
( ).
n
n
f x
f x
x
x
f x
x
j
j
j
³
ì
ï
=
Û
³
í
ï
=
î
2.
2
2
( )
0,
( )
( )
( )
0,
( )
( ).
n
n
f x
f x
x
x
f x
x
j
j
j
ì
³
ï
=
Û
³
í
ï
=
î
3.
2
( )
(
0)
.
n
f x
a a
x
=
< Þ ÎÆ
4.
2
1
2
1
( )
( )
( )
( )
n
n
f x
x
f x
x
j
j
+
+
=
Û
=
. 5.
2 1
2 1
( )
( )
( )
( )
n
n
f x
x
f x
x
j
j
+
+
=
Û
=
.
6.
(
)
2
( )
0,
(
0),
( )
0,
( )
( )
( )
( )
.
f x
a
x
f x
x
a
f x
a
x
j
j
j
³
³
³
ìï
-
= Û í
=
+
ïî
7.
(
)
2
( )
0, ( )
0,
( )
0,
( )
( )
(
0)
( )
( )
.
f x
x
b
x
f x
x
b b
f x
b
x
j
j
j
j
ì
³
³
-
³
ï
+
=
³
Û í
=
-
ïî
Irrasional tengsizliklar
Irrasional tengsizliklar quyidagicha ekvivalent almashtirish
yordamida yechiladi
(
)
n
N
Î
:
1.
2
2
( )
0,
( )
( )
( )
0,
( )
( ).
n
n
f x
f x
g x
g x
f x
g
x
ì
³
ï
<
Û
>
í
ï
<
î
2.
2
2
( )
0,
( )
( )
( )
0,
( )
( ).
n
n
f x
f x
g x
g x
f x
g x
³
ì
ï
<
Û
³
í
ï
<
î
3.
2 1
2 1
( )
( )
( )
( ).
n
n
f x
g x
f x
g
x
+
+
<
Û
<
4.
2 1
2 1
( )
( )
( )
( ).
n
n
f x
g x
f x
g x
+
+
<
Û
<
5.
2
2
( ) 0,
( ) 0,
( )
( )
( ) 0,
( )
( ).
n
n
g x
f x
f x
g x
g x
f x
g
x
é
<
ì
í
ê
³
î
ê
>
Ûê
³
ìï
êí
ê
>
ïî
ë
6.
2 1
2 1
( )
( )
( )
( ).
n
n
f x
g x
f x
g
x
+
+
>
Û
>
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
29
7.
2
2
2
( )
0,
( )
0,
( )
1
( )
0,
( )
( )
( ).
( )
( )
n
n
n
g x
g x
f x
f x
g x
f x
g
x
f x
g
x
ì
<
>
ì
ï
ï
> Û
³
í
í
>
ïî
ï
<
î
U
8.
2
2
( )
0, ( )
0,
( )
0,
( )
1
( )
0
( )
( )
( ).
n
n
g x
f x
g x
f x
f x
g x
f x
g
x
>
³
ì
<
ì
ï
< Û í
í
³
<
ï
î
î
U
Arifmetik progressiya
1.
n
-
hadini topish formulasi:
(
)
1
1
, ,
n
a
a
n
d
n
N
= + -
Î
bu yerda
d
- ayirmasi,
1
a
- birinchi hadi,
n
a
n-chi hadi,
n
-
hadlari soni.
2.
d
- ayirmani toppish:
2
1
3
2
4
3
1
...
n
n
d
a
a
a
a
a
a
a
a
-
= - = - = - = = -
yoki
(
)
(
)
n
m
d
a
a
n
m
=
-
-
.
3. Xossalari:
a)
1
1
2
k
k
k
a
a
a
-
+
+
=
yoki
2
n k
n k
n
a
a
a
-
+
+
=
tenglik bajarilsa
{ }
n
a
ketma-ketlik arifmetik progressiya bo’ladi;
b)
(
)
; ;
n
m
n
m
k
p
a
a
n m d
a
a
a
a
n m
k
p
-
=
-
+
=
+
« + = +
v)
1
2
1
3
2
1
...
;
n
n
n
n k
k
a
a
a
a
a
a
a
a
-
-
-
+
+
=
+
=
+
= =
+
4. Dastlabki
n
ta hadi yig’indisi -
n
S
:
1)
1
2
3
...
;
n
n
S
a
a
a
a
= +
+ + +
2)
1
;
n
n
n
S
S
a
-
-
=
3)
1
1
(
)
2
(
1)
;
2
2
n
n
n
a
a
n
a
d n
S
S
n
+
+
-
=
=
×
;
(
1) 2
n
n
S
n a
+
= ×
;
4)
n k
n
k
S
S
S
n k d
+
=
+
+ × ×
; 5)
(
)
,
m n
m
n
m
n
S
S
S
m
n
m
n
+
+
=
-
¹
-
;
6)
(
1),
k
n
n
S
S
d n k
= + × × -
k
n
S
-
n dan k
gacha bo`lgan sonlar yig;
7)
2
4
2
1
3
2
1
...
...
n
n
a
a
a
a
a
a
n d
-
+
+
+
=
+
+
+
+ ×
;
Geometrik progressiya
1.
n
-
hadini topish formulasi:
1
1
,
,
n
n
b
b q
n
N
-
=
Î
bu yerda
q
-maxraji,
1
b
- birinchi hadi,
n
b
n-chi hadi, n - hadlari soni.
Click here to buy
A
B
B
Y
Y
PD
F Transfo
rm
er
2
.0
w
w
w .A
B B Y Y.
c o
m
Do'stlaringiz bilan baham: |
