|
2
6
9;
y
x
x
=
-
+
4)
2
4
4;
y
x
x
=
+
+
5)
2
2
(
1)
1) ;
y
x
x
=
-
+
+
6)
2
4
4 |
2| .
y
x
x
x
=
-
+ +
+
515.
Tenglamaning haqiqiy ildizlarini toping:
1)
2
|
| 2
0;
x
x
-
- =
2)
2
4 |
| 3
0;
x
x
-
+ =
3)
2
|
| 2;
x
x
-
=
4)
2
|
| 1;
x
x
+
=
5)
2
|
2 | 2;
x
-
=
6)
2
|
26 | 10.
x
-
=
516.
Ildiz chiqaring:
1)
5
19
32
7 ;
2)
4
9
5 ;
3)
6
3
9
8
343
,
0;
b
a
a
¹
4)
8
4
4
16
81
,
0.
x
y
y
>
517.
Soddalashtiring:
1)
(
)
3 20 7 15
5 : 5;
+
-
2)
(
)
3
3
3
3
7
14
56 : 7;
-
+
3)
3
2
2
3
2
6 3
;
+
-
4)
3
4
7 1
7 0,5 343.
-
+
518.
Ifodalarning qiymatlarini taqqoslang:
1)
( )
( )
1/3
1/2
5
5
3
3
va
;
-
-
2)
0,3
0,37
(2 0,5) va (2 0,5)
.
519
. Ifodani soddalashtiring:
1)
6
3
1
2
9
;
a a
a
-
-
2)
4
3 3
1
3
;
x
x
x
3)
3
4
4
(16
) ;
a
-
-
4)
2
6 3
(27
) .
b
-
520.
Ildiz belgisi ostidan ko‘paytuvchini chiqaring:
1)
2
9
, bunda
0,
0;
a b
a
b
<
>
2)
2 3
25
, bunda
0,
0;
>
>
a b
a
b
3)
3 5
8
, bunda
0,
0;
a b
a
b
<
<
4)
3 3
12
, bunda
0,
0.
a b
a
b
<
<
191
521.
Ko‘paytuvchini ildiz belgisi ostiga kiriting:
1)
5, bunda
0;
³
x
x
2)
3, bunda
0;
<
x
x
3)
3, bunda
0;
a
a
-
³
4)
5, bunda
0.
a
a
-
<
522.
Hisoblang:
1)
1
1
0,25
0
3
3
10
13
1000 (0,0001)
(0,027) 7,1
;
-
æ ö
×
+
×
- ç ÷
è ø
2)
( )
( )
2
1
1
3
2
10
1
27
1
11
9
2
:
(6,25) :
4 .
-
-
+
-
523.
Ifodaning qiymatini toping:
1)
1
1 1
1 1
2
2 2
2 2
1
1
2
2
2
bunda
3,
12.
-
+
-
-
æ
ö
ç
÷
-
×
=
=
ç
÷
ç
÷
è
ø
a
a b
a
a b
a
b
a
a
b
b
a
b
2)
2
, bunda
5,
20.
+
+
+
×
-
=
=
-
+
m
mn
n
mn
n
m
m
n
n
m n
m
n
524.
Tenglamani yeching:
1)
1
1
5
3
2
2
2
2;
2)
3;
3)
8;
4)
0.
x
x
x
x
-
-
=
=
=
=
525.
25
x
y
= -
funksiyaning grafigiga:
1) ( 5; 5 5);
2) ( 5 2; 5 2)
A
B
-
-
nuqta tegishli bo‘lish yoki bo‘lmasligini aniqlang.
526.
1 2
y
x
=
-
funksiyaning grafigiga: 1)
1
2
4
2
;
;
æ
ö
ç
÷
è
ø
C
2)
1
2
;1
æ
ö
-
ç
÷
è
ø
D
nuqta tegishli bo‘lish yoki bo‘lmasligini aniqlang.
527.
Funksiyaning aniqlanish sohasini toping:
1)
2
4
3
7
4
3
2
6
3
10;
2)
;
3)
;
-
+
-
-
= -
-
+
=
=
x
x
x
x
y
x
x
y
y
4)
2
6
5
2
15
6
0, 5
1
4
;
5)
;
6)
.
+
+
-
=
=
=
x
x
x
x
x
y
y
y
192
528.
Funksiyaning grafigini yasang:
1)
2
6
10;
=
+
+
y
x
x
2)
2
7
6;
= -
-
-
y
x
x
3)
4
;
=
x
y
4)
6
;
x
y
= -
5)
2
2
;
=
x
y
6)
4
1
4
.
=
y
x
Qaysi oraliqlarda funksiyaning o‘sishi, kamayishini grafik bo‘yi-
cha aniqlang; funksiyaning juft yoki toqligini aniqlang.
529.
P
(1; 0) nuqtani: 1)
A
(0; 1); 2)
B
) (0; –1); 3)
C
(–1; 0); 4)
D
(1; 0)
nuqtaga o‘tkazadigan bir necha burish burchaklarini ko‘rsating.
530
. Hisoblang:
2sin
cos
tg
4
3
3
ctg
sin
cos
6
6
4
p
p
p
+
-
p
p
p
-
-
.
531.
Sonning musbat yoki manfiy ekanligini aniqlang:
1)
4
5
5
6
sin sin
co s ;
p
p
p
2)
2
sin cos(
)tg , 0
.
p
a
p + a
a
< a <
532.
Berilgan:
3
2
2
sin
0,6, sin
0,28, 0
,
.
p
p
a =
b = -
< a <
p < b <
Hisoblang: 1) cos(
); 2) sin(
).
a - b
a + b
533.
Ko‘paytuvchilarga ajrating:
1) sin2
2sin ;
a -
a
2)
2
sin
sin ;
a
a +
3)
cos
sin2 ;
a -
a
4)
2
1 sin2
cos
.
-
a -
a
534.
Agar
8
2
17
2
cos
va sin
0 bo‘lsa, sin , cos , tg
a
a
= -
<
a
a
a
ni hisob-
lang.
535.
Agar
1)
1
10,
6,
23;
=
=
=
a
d
n
2)
1
1
2
42,
,
12;
a
d
n
=
=
=
3)
1
0,
2,
7;
=
= -
=
a
d
n
4)
1
1
2
3
3
,
,
18
a
d
n
=
=
=
bo‘lsa, arifmetik progressiyaning
n
- hadini va dastlabki
n
ta
hadining yig‘indisini hisoblang.
536.
Agar
a
1
= 2,
a
n
= 120,
n
= 20 bo‘lsa, arifmetik progressiyaning
dastlabki
n
ta hadi yig‘indisini toping.
193
537.
n
- hadi
n
n
a
-
=
1 2
3
formula bilan berilgan ketma-ketlik arifmetik
progressiya bo‘lishini isbotlang.
538.
Agar geometrik progressiya uchun
1)
b
1
= 5 va
q
= –10 bo‘lsa,
b
4
ni toping;
2)
b
4
= –5000 va
q
= –10 bo‘lsa,
b
1
ni toping.
539.
Agar:
1)
1
3,
2,
5;
b
q
n
=
=
=
2)
b
1
= 1,
q
= 5,
n
= 4;
3)
1
1
4
8,
,
4
b
q
n
=
=
=
;
4)
b
1
= 1,
q
= –3,
n
= 5
bo‘lsa, geometrik progressiyaning
n
- hadini va dastlabki
n
ta
hadi yig‘indisini hisoblang.
540.
Agar
1
1
4
,
2,
6
b
q
n
=
=
=
bo‘lsa, geometrik progressiya dast-
labki
n
ta hadining yig‘indisini toping.
541
. Cheksiz kamayuvchi geometrik progressiya yig‘indisini toping.
1)
8
3
6, 4, , ...;
2)
1
5
5, 1, , ...;
-
3)
4)
1
1
1
2
4
8
, , , ...
5)
2
2
2, 1,
, ...;
6)
5
5
5,
1,
,...
-
-
-
542.
Ildiz belgisi ostidan ko‘paytuvchini chiqaring:
1)
4
20
, bunda
0,
0.
a b
a
b
<
>
2)
3
3 4
8
, bunda
0,
0.
a b
a
b
<
>
3)
2
(
1) , bunda
1;
-
<
a
a
4)
2
(3
) , bunda
3.
+
> -
a
a
543.
Ifodani soddalashtiring:
1)
2
(
)
, bunda
;
a b
a
b
a b
-
>
-
2)
2
(
)
, bunda
;
a b
b
a
a b
-
>
-
3)
2
2
1
1
1
1
, bunda
0;
x x
x
x
x
+ +
+ +
>
4)
2
2
1
1
1
1
, bunda
0.
x x
x
x
x
+ +
+ +
<
13 – Algebra, 9- sinf uchun
-
1
1
4
16
1,
,
,...,
194
544.
Tengliklardan qaysinisi to‘g‘ri:
7 4 3
2
3 mi yoki
7 4 3
3 2
-
= -
-
=
-
mi?
545.
Maxrajdagi irratsionallikni yo‘qoting:
1)
3
1
2
3
;
+
2)
4
1
;
-
b
a
3)
3
3
1
3
2
;
-
4)
2
.
5
5
+
546.
Ifodani soddalashtiring:
1)
2
4
2
4
1 2
4
4
(
2)
;
ab
a
a
a
a b
a
-
+
+
-
-
2)
2
;
b
a
b
b
a
a
ab
ab
ab
-
+
-
æ
ö
-
×
ç
÷
è
ø
3)
(
)
1
1
1
1
4
4
2
2
1
3
1 1
1
1
1
2
4
2 4
4
4
;
a
b
a
b
a
b
a b
a
a b
a
a
-
+
+
-
+
æ
ö
-
ç
÷ ×
-
ç
÷
ç
÷
è
ø
4)
3
3
2
2
1
1
2
2
.
a
b
a
b
a
b
a
b
ab
a
b
+
+
-
-
æ
ö
-
ç
÷
-
×
ç
÷
ç
÷
è
ø
547.
2
4
=
x
y
funksiyaning
x
> 0 oraliqda o‘sishi yoki kamayishini aniqlang.
548.
Funksiyaning aniqlanish sohasini toping.
1)
(
2)(
3);
=
-
-
y
x
x
2)
2
(
6 ;
=
-
y
x
x
3)
2
1
;
2 2
2
x
x
y
-
+
=
4)
2
3
;
2 3
3
x x
y
- +
=
5)
(
1)
;
5
x
x
x
y
-
+
=
6)
2
2
9
2
.
x
x
x
y
-
-
=
549.
Funksiyaning grafigini yasang va grafik bo‘yicha uning asosiy
xossalarini aniqlang:
1)
3
;
1
x
y
+
=
2)
1
;
2
x
y
-
=
3)
2
;
x
x
y
+
=
4)
3
;
x
x
y
-
=
5)
3;
y
x
=
-
6)
3
2
.
y
x
=
-
550.
Tenglamani yeching:
1)
2
4; 2)
3
8;
3) 2
1
1;
x
x
x
x
- =
+ =
+ =
-
4) 3
1 3 ;
x
x
-
=
+
5)
4
3
2
2
12
;
6) 6
.
x
x
x x
x
+
=
-
=
551
. Ifodani soddalashtiring:
1)
2
2
t g
;
1 ctg
a
+
a
2)
2
2
1+ctg
;
ctg
a
a
3)
2
2
tg
tg
;
ctg
ctg
4) (tg
ctg )
(tg
ctg ) .
a- b
a+
b
a +
a -
a -
a
195
552.
Ifodani soddalashtiring:
1)
3
ctg
: sin
sin(
4
2
tg(
)(cos(
2 )
sin(
2 ))
;
p
a -
a - p -
p + a
p + a
a + p +
a - p
æ
ö
æ
ö
æ
ö
ç
÷ ç
÷
ç
÷
è
ø
è
ø
è
ø
2)
( )
( )
3
3
2
2
sin(
2 )cos
tg(
)tg
.
x
x
x
x
p
-
p +
- p
+
p -
553
. Tenglamani yeching:
1)
x
x
x
x
-
-
=
+
+
=
2
1 cos
2sin
0;
2) 1 cos2
2cos
0.
554.
Ayniyatni isbotlang:
1)
a-b + b
a+b
a+b +
a-b
a+b - b
a-b
a+b +
a-b
=
=
a
tg(
) tg
cos(
)
sin(
) sin(
)
tg(
) tg
cos(
)
cos(
) cos(
)
;
2)
tg .
555.
Ayniyatni isbotlang:
1)
( )
2
4
2
1 sin
2cos
;
p a
-
+
a =
2)
( )
2
4
2
1 sin
2sin
.
p a
-
-
a =
556.
Uchburchakning ichki burchaklari ayirmasi
8
p
ga teng bo‘lgan
arifmetik progressiyaning ketma-ket uchta hadi bo‘ladi. Shu
burchaklarni toping.
557.
Arifmetik progressiyada
1
5
3 4
5
65
;
.
3
72
a
a
a a
+
=
=
Progressiyaning
dastlabki o‘n yettita hadining yig‘indisini toping.
558.
Ikkinchi hadi birinchisidan 35 ga kam, uchinchi hadi esa
to‘rtinchisidan 560 ga ortiq bo‘lgan geometrik progressiyaning
dastlabki to‘rtta hadini toping.
559.
Geometrik progressiyada
q
= 3,
S
6
= 1820 bo‘lsa,
b
1
va
b
5
ni toping.
560.
Cheksiz kamayuvchi geometrik progressiyaning yig‘indisi
8
5
ga
teng, ikkinchi hadi
1
2
-
ga teng. Uchinchi hadini toping.
561
. Arifmetik progressiyaning ketma-ket hadi bo‘lgan uchta sonning
yig‘indisi 39 ga teng. Agar birinchi sondan 4 ni, ikkinchisidan
5 ni, uchinchisidan esa 2 ni ayirilsa, hosil bo‘lgan sonlar geometrik
progressiyaning ketma-ket uchta hadi bo‘ladi. Shu sonlarni
toping.
196
Ifodani soddalashtiring
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