|
5. Funksiyalar va grafiklar
638.
A
nuqta quyida berilgan funksiyalarning grafigiga tegishli yoki
tegishli emasligini aniqlang; shu funksiyalarning koordinata
o‘qlari bilan kesishish nuqtalari koordinatalarini va
x
= –2 bo‘l-
ganda funksiyalarning qiymatini toping:
1)
y
= 3 – 0,5
x
,
A
(4; 1);
2)
1
2
4
y
x
=
-
,
A
(6; –1);
3)
y
= 2,5
x
– 5,
A
(1,5; –1,25); 4)
y
= –1,5
x
+ 6,
A
(4,6; –0,5).
639.
Funksiyalarning grafigini yasang (bitta koordinata tekisligida):
1)
y
= 3
x
,
y
= –3
x
;
2)
1
1
3
3
,
y
x y
x
=
= -
;
3)
y
=
x
– 2,
y
=
x
+ 2;
4)
y
= –
x
– 2,
y
= 2 –
x
.
640.
Funksiyaning grafigini yasang:
1)
2
1
4
2
y
x
=
+
;
2)
( )
2
1
3
y
x
=
-
;
3)
(
)
2
1
4
2,5
y
x
=
+
-
;
4)
y
=
x
2
– 4
x
+ 5;
5)
y
=
x
2
+ 2
x
– 3; 6)
y
= –
x
2
– 3
x
+ 4.
641.
Parabola uchining koordinatalarini toping:
1)
y
=
x
2
– 8
x
+16;
2)
y
=
x
2
– 10
x
+ 15;
3)
y
=
x
2
+ 4
x
– 3;
4)
y
= 2
x
2
– 5
x
+ 3.
642.
Funksiyaning eng katta va eng kichik qiymatlarini toping:
1)
y
=
x
2
– 7
x
– 10;
2)
y
= –
x
2
+ 8
x
+ 7;
3)
y
=
x
2
–
x
– 6;
4)
y
= 4 – 3
x
–
x
2
.
643.
Berilgan ikkita funksiyaning bitta koordinata tekisligida grafik-
larini yasang va
x
ning qanday qiymatlarida bu funksiyalarning
qiymatlari tengligini aniqlang:
1)
y
=
x
2
– 4 va
y
= 3
x
;
2)
y
= (
x
+ 3)
2
+ 1
va
y
= –
x
.
207
644.
Grafikning xomaki tasvirini yasang va funksiyaning xossalarini
ayting:
1)
y
=
x
4
; 2)
y
=
x
5
; 3)
3
1
x
y
=
; 4)
4
1
x
y
=
.
645.
Ifodalarning qiymatlarini taqqoslang:
1)
4
5,3 va
4
1
3
5 ;
2)
5
2
9
-
va
5
1
7
-
.
646.
Funksiyaning grafigini yasang va
x
ning
y
= 0,
y
> 0,
y
< 0
bo‘ladigan qiymatlarini toping:
1)
y
= 2
x
2
– 3;
2)
y
= –2
x
2
+ 1;
3)
y
= 2(
x
– 1)
2
;
4)
y
= 2(
x
+ 2)
2
;
5)
y
= 2(
x
– 3)
2
+ 1;
6)
y
= –3(
x
– 1)
2
+ 5.
6. Trigonometriya elementlari
647.
1)
(
)
2
2
2
2
;
-
; 2)
(
)
2
2
2
2
;
-
-
; 3)
(
)
1
3
2
2
;
-
-
; 4)
(
)
3
1
2
2
;
-
-
koordinatali nuqta hosil qilish uchun
P
(1; 0) nuqtani burish
kerak bo‘lgan barcha burchaklarni toping.
648.
Ifodani soddalashtiring:
1
sin cos
(1 tg )(1 ctg )
a
a
+
a
+
a -
.
649.
Ayniyatni isbotlang:
1)
2
2
1 (sin
cos )
sin cos
ctg
2tg
-
a+
a
a
a-
a
=
a
;
2)
2
2
tg
sin cos
1
2
(sin
cos )
1
tg
a-
a
a
a-
a -
= -
a
.
650.
Ifodani soddalashtiring:
1) sin
2
(
a
+ 8
p
) + cos(
a
+ 10
p
); 2) cos
2
(
a
+ 6
p
) + cos
2
(
a
– 4
p
).
651.
Ifodani soddalashtiring:
2
2
sin 2
sin cos(
)
2(1 2 cos
)
1 2 sin
a
a
p-a
-
a
-
a
+
.
652.
Ayniyatni isbotlang:
2
2
cos
sin
1 sin
1 cos
sin
cos
x
x
x
x
x
x
-
+
-
=
+
.
653.
1) agar
3
3
cos
a = -
va
2
p
< a < p
bo‘lsa, sin2
a
ni hisoblang;
2) agar
1
3
sin
a =
bo‘lsa, cos2
a
ni hisoblang.
208
654.
Ifodaning qiymatini toping:
1) cos765
°
– sin750
°
– cos1035
°
; 2)
11
19
3
3
sin
cos 690
cos
p
p
+
° -
.
655.
Agar tg
a
= 2 bo‘lsa, ifodaning qiymatini toping:
1)
2
2
sin
sin cos
cos
3 cos sin
a+
a
a
a+
a
a
;
2)
2
2
2 sin
3 cos
-
a
+
a
.
656.
tg
a
+ ctg
a
= 3 ekanligi ma’lum. tg
2
a
+ ctg
2
a
ni toping.
657.
Ifodani soddalashtiring:
1)
cos
sin
cos
sin
4
tg
a +
a
p
æ
ö
ç
÷
a -
a
è
ø
-
+ a
;
2)
2
1 sin 2
1 sin 2
4
tg
-
a
p
æ
ö
ç
÷
+
a
è
ø
- a -
.
658.
Ifodani soddalashtiring:
2
cos 2
sin 2
2 cos
cos(
) cos(2,5
)
a -
a -
a
-a -
p+a
.
7. Progressiyalar
659.
Agar
a
1
= 7,
a
7
= –5 bo‘lsa, arifmetik progressiyaning ayirmasini
toping.
660.
Agar
a
10
= 4,
d
= 0,5 bo‘lsa, arifmetik progressiyaning birinchi
hadini toping.
661
. Agar: 1)
a
n
= 459,
d
= 10,
n
= 45; 2)
a
n
= 121,
d
= –5,
n
= 17
bo‘lsa, arifmetik progressiyaning birinchi hadini va dastlabki
n
ta hadining yig‘indisini hisoblang.
662.
Agar arifmetik progressiyada
a
1
= –2,
a
5
= –6,
a
n
= –40 bo‘lsa,
n
nomerni toping.
663
.
n
n
b
b
+
= -
1
2
formula va
b
1
= 1024 shart bilan berilgan ketma-ket-
likning dastlabki o‘nta hadining yig‘indisini toping.
664.
Agar geometrik progressiyada:
1)
b
1
= 5,
q
= –10 va
b
n
= –5000 bo‘lsa,
n
ni;
2)
b
3
= 16 va
b
6
= 2 bo‘lsa,
q
ni;
3)
b
3
= 16 va
b
6
= 2 bo‘lsa,
b
1
ni;
4)
b
3
= 16 va
b
6
= 1 bo‘lsa
b
7
ni toping.
665
. Agar 3 + 6 + 12 + ... + 96 yig‘indining qo‘shiluvchilari geometrik
progressiyaning ketma-ket hadlari bo‘lsa, shu sonlar yig‘indisini
toping.
209
666.
Agar:
1)
3
10
25,
3;
a
a
=
= -
2)
1
7
10,
19;
a
a
=
=
3)
3
7
2
14
4,
8;
a
a
a
a
+
=
+
= -
4)
+
=
×
=
2
4
1
5
16,
28
a
a
a a
bo‘lsa, arifmetik progressiyaning birinchi hadini va ayirmasini
toping.
667.
Agar: 1)
a
9
= –5 va
a
11
= 7; 2)
a
9
+
a
11
= –10; 3)
a
9
+
a
10
+
a
11
= 12
bo‘lsa, arifmetik progressiyaning o‘ninchi hadini toping.
668
.
S
7
= –35 va
S
42
= –1680 bo‘lsa, arifmetik progressiyaning birinchi
hadini va ayirmasini toping.
669
. n-
hadining formulasi bilan berilgan ketma-ketlik geometrik
progressiya bo‘la oladimi:
1)
b
n
= –3
2
n
; 2)
b
n
= 2
3
n
; 3)
n
n
n
n
n
b
b
-
=
=
( 1)
3
2
2
;
4)
?
670.
Agar: 1)
b
1
= 12,
S
3
= 372;
2)
b
1
= 1,
S
3
= 157;
bo‘lsa, geometrik progressiyaning maxrajini hisoblang.
671
. Agar
2
4
1
1
2
72
va
b
b
= -
= -
bo‘lsa, geometrik progressiyaning
birinchi hadini, maxrajini va
n
- hadining formulasini toping.
672
. Agar
b
3
= –6 va
b
5
= –24 bo‘lsa, geometrik progressiyaning
to‘rtinchi hadini va maxrajini toping.
673
.
1
3
va 27 sonlari orasiga uchta sonni shunday joylashtiringki,
natijada geometrik progressiyaning ketma-ket beshta hadi hosil
bo‘lsin.
674.
Agar geometrik progressiyada:
1)
q
= 3,
S
3
= 484 bo‘lsa,
b
1
va
b
5
ni toping;
2)
b
3
= 0,024,
S
3
= 0,504 bo‘lsa,
b
1
va
q
ni toping.
675
. Agar:
1)
b
1
+
b
2
= 20,
b
2
+
b
3
= 60; 2)
b
1
+
b
2
= 60,
b
1
+
b
3
= 51
bo‘lsa, geometrik progressiyaning birinchi hadini va maxrajini
hisoblang.
676
. Agar geometrik progressiyada:
1)
b
4
= 88,
q
= 2 bo‘lsa,
S
5
ni;
2)
S
5
= 341,
q
= 2 bo‘lsa,
b
1
ni;
3)
b
1
= 11,
b
4
= 88 bo‘lsa,
S
5
ni;
4)
b
3
= 44,
b
5
= 176 bo‘lsa,
S
5
ni
toping.
14 – Algebra, 9- sinf uchun
210
Do'stlaringiz bilan baham: |
