Sonning butun qismi
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Smith1 Mavzu:
Sonning butun
qismi](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_1.png)
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Smith2 Maqsad :
Sonning butun qismi funksiyasi bilan tanishish
Sonning butun qismi funksiyasi grafigini yasash
Mustaqil misollar yecha olish ko` nik masini shakllantirishButun qism funksiyasi qo` llanilishiga doir misollar yechish . 1
2
3
4](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_2.png)
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Smith3Sonning butun qismi
Sonning butun qismi deb, shu
sondan katta bo`lmagan butun
sonlar ichida eng kattasiga
aytiladi va [x] kabi belgilanadi.
Masalan, [3,45]=3, [-2,5]=-3,
[2]=2 , [0.23]=0](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_3.png)
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Smith4Sonning butun qismi
Sonning butun qismi funksiyasi
“ant`ye” funksiyasi deb ham
ataladi.](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_4.png)
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Smith5 y=[x] funksiya grafigi
ZyZxE RxRyD
,)( ,)(](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_5.png)
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Smith6Ant`ye funksiyasi xossalari:
.,,y-x holda u bo`lsa, [y][x] Agar 6. Z; R,xagar m,x][][x. [0;1); Z,xagar x,]4.[x R;xagar 1,x][x[x] 3. R;xagar x,[x]1-x 2. Z;xagar x,[x] 1.
Ryxmm
15 ](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_6.png)
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Smith7 1
n sonidan k at t a bo` l maga n nat ural sonl ar i chida
necht asi k soniga qoldiqsiz bo` linadi?
k n
•
100 dan katta bo`lmagan natural sonlar ichida nechtasi 7 ga
qoldiqsiz bo`linadi?
14
7100
](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_7.png)
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Smith8 1
[n;m ] k esmada joy l ashgan
sonlardan necht asi k soniga qol diqsiz
bo` linadi? Nnm ,
kn
km 1
•
Barcha uch xonali natural sonlar ichida nechtasi 7 ga
qoldiqsiz bo`linadi?128 14 142
7
99
7
999
](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_8.png)
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Smith9 1
•
1 dan N gacha natural sonlar ichida nechtasi a ga ham, b ga
ham bo`linmaydi ?
b a
N
b
N
a
N
N](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_9.png)
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Smith10 1
1 da n 100 gacha sonl ar i chida necht asi 2 ga ham, 3 ga ham
bo` li nmay di?33 16 33 50 100 3 2
100
3
100
2
100 100
16 3 2
100 3 2
33 3
100 3
50 2
100 2
) (
sonlar igan bo`linmayd ham ga 3 ham, ga 2
`
`
`
sonlar linadigan bo ga va ga
sonlar linadigan bo
sonlar linadigan bo](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_10.png)
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Smith11 1
•
1 dan N gacha natural sonlar ichida nechtasi a ga ham, b
ga ham, c ga ham bo`linmaydi ?
c b a
N
c a
N
c b
N
b a
N
c
N
b
N
a
N N](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_11.png)
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Smith12 1
•
1 dan 100 gacha natural sonlar ichida nechtasi 2 ga ham,
3 ga ham, 5 ga ham bo`linmaydi ?
26310616203350100 532 100
52100
53100
32100
5100
3100
2100
100
)(](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_12.png)
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Smith13 •
21! ni tub ko`paytuvchilarga ajrating.
8765
43
21
1917131175322120432121 ...!
18 1 2 5 10 2
21
2
21
2
21
2
21
2
21 5 4 3 2 1
...
927
3 21
3 21
321
322
1
19 21
1
17 21 1
13 21
1
11 21 3
721
4
521
87 65 43
111134918
19171311753221 !](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_13.png)
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Smith14 DTM 2019
toping. qiymatini ning n bo`lsa, son toq ifoda
411!
son. butunmusbat - n
n
nn CC
28
2
22
22 1
n
411!Suratdagi ifodada 2 ning darajasini aniqlaymiz
8 1 2 5 2
11
2
11
2
11
3 2 1
2n=8
n=4](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_14.png)
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Smith15 DTM 2019
toping. qiymatini kichik eng ning b bo`lsa,
! !
A 7aA
Agar sonlardir. natural b va a b
42150
a
B C
A
18
624
7
77
42150
! !
b=18 6
742 24321
7150
7150
2
](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_15.png)
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Smith16 toping qiymatini katta eng ning n bo`ladigan son natural ifoda !
n
640 n n n n
C C
3 2
3 2 3 2
6
40 18 38 18 38
3 2
!
n=18
yetarli ko`rish darajasini gkattasinin sonlaridan b va a uchun bo`linishi qoldiqsiz ga ba ifoda.... n
3
21
532 ](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_16.png)
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Smith17 DTM 2019
nnn
52 52
52 52
0
!
)( !
1 52!
n
n=12
Berilgan son 12 ta nol bilan tugaydi.52! ifoda nechta nol bilan tugaydi?
Bu sonni 10 ning qanday eng katta darajasiga bo`linishini topishimiz
yetarli12 2 10 5
52
5
52 2
](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_17.png)
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Smith18 DTM 2019 toping. qiymatini kichik eng ning b
bo`lsa, 60! sonlardir. natural b va a b a 21
bbb
7321 C 928
7360 !
Ca bb
928
7373
b=9](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_18.png)
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Smith19 •
Tenglama yechimga ega bo`lishi uchun n soni albatta
butun bo`lishi kerak! Aks holda tenglama yechimga
ega bo`lmaydi
yechiladi keltirilib katengsizlik 1nxn tenglamani n[x] ko`ra xossasiga funksiyasi qismi butun Sonning
yeching tenglamani n[x] ](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_19.png)
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Smith20 •
Javob: (-4;-1,5] ],;(
);( );(],;(1-x 5x
yeching Tenglamani
514
14 151
0
1 4 0
1 32
4
15 3
15 43 3
15
xx x x
x xx x x x](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_20.png)
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Smith21 5 4
15 7 5 4
1
5 715 15 7
0
5 715 31
30 1 30 131
40403910 403910
1
40 3910 40 3910 1
40 3910
40 3910 15 75
8 6
8 5 15 75
5 715 5 715
21
xxjavob xx xx t tt
tt tt
tt tt tt
ttt tt t
xtx x
,: ko`ramiz xollarni 1t va 0t nekanligida son butunt , ,8 6x5
son. butunt Bunda•kiritamiz. Belgilash• 8 6x5
yeching Tenglamani](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_21.png)
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Smith22 1
2 142 14 2 14
4 12 4
tt
t tt t
xtx 12x
[x]yeching tenglamani 1 2x- 4[x] ](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_22.png)
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Smith23 chizamiz nigrafiklari funksiya yechamiz. usulda grafik va olamiz keltirib shaklga 12x
[x] Tenglamani
4 12 4
x
y xy
yeching tenglamani 1 2x- 4[x]
Grafiklar bitta nuqtada
kesishadi. x=1,5](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_23.png)
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Smith2462, 3 x
5x yeching Tenglamani
olmaydi bo`la teng ga 2,6 qismi butun sonning sababi emas, ega yechimga Tenglama](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_24.png)
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Smith25 Test
teng? nechaga yig`indi cba bo`lsa, o`rinli tenglik 5328!-6! uchunsonlar butunmusbat c va b a, 1. cb
a
2
a) 11
b) 12
c) 10
d) 9](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_25.png)
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Smith26 Test
a) 81
b) 82
c) 80
d) 90•
2. Nechta uch xonali natural son 11 ga qoldiqsiz bo`linadi?](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_26.png)
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Smith27 Test
a) 10
b) 11
c) 8
d) 18•
3. 25! soni 3 ning qanday eng katta darajasiga qoldiqsiz
bo`linadi?](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_27.png)
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Smith28 Test
a) 10
b) 11
c) 14
d) 12•
4. 23∙24∙…∙60 soni 5 ning qanday eng katta darajasiga
qoldiqsiz bo`linadi?](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_28.png)
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Smith29 Test
a) 131
b) 130
c) 150
d) 69•
5. 200 dan katta bo`lmagan natural sonlardan nechtasi 2
ga ham, 5 ga ham, 7 ga ham bo`linmaydi?](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_29.png)
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Smith30 Test
a) 1
b) 3
c) 4
d) 2•
6. [x]=3 bo`lsa, x nechta butun qiymat qabul qila oladi?](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_30.png)
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Smith31 Test
a) 4,6
b) 1,6
c) 2,6
d) 5,6•
7. Hisoblang [-3,25]+1,6+[7,25]=](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_31.png)
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Smith32 Test
a) -3
b) -4
c) -2
d) -5 359919908 )(,,. Hisoblang](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_32.png)
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Smith33 Test
a) 2
b) 3
c) 0
d) 1 59
4 13-3x
bor ildizi butun nechta ngTenglamani.
337
11 37333 2413320 6
x x x 4 13-3x
5](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_33.png)
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Smith34 Test
a) [-7,5;-5,5)
b) [-7,5;-5,5]
c) (-7,5;-5,5)
d) (-7,5;0] 210
2 3,5x
yeching Tenglamani.](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_34.png)
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Smith35 Xulosa
•
Sonning butun qismi funksiyasi umumiy o`rta ta`lim
maktablarida chuqur o`rganilmaydi. Faqatgina sonning
butun qismini topish topishga doir ma`lumotlar keltirilgan.
Lekin yuqorida ko`rib o`tilgan va shunga o`xshash misollar
orqali o`quvchilarni yanada fanga qiziqtirish mumkin.
•
Bu tipdagi misollarni darsdan tashqari mashg`ulotlarda
ko`rib chiqish tavsiya etiladi.](/data/documents/0a5f2e46-ebb5-4421-8ca7-b243e519eebd/page_35.png)
i9 presentation to Joe Smith1 Mavzu: Sonning butun qismi
i9 presentation to Joe Smith2 Maqsad : Sonning butun qismi funksiyasi bilan tanishish Sonning butun qismi funksiyasi grafigini yasash Mustaqil misollar yecha olish ko` nik masini shakllantirishButun qism funksiyasi qo` llanilishiga doir misollar yechish . 1 2 3 4
i9 presentation to Joe Smith3Sonning butun qismi Sonning butun qismi deb, shu sondan katta bo`lmagan butun sonlar ichida eng kattasiga aytiladi va [x] kabi belgilanadi. Masalan, [3,45]=3, [-2,5]=-3, [2]=2 , [0.23]=0
i9 presentation to Joe Smith4Sonning butun qismi Sonning butun qismi funksiyasi “ant`ye” funksiyasi deb ham ataladi.
i9 presentation to Joe Smith5 y=[x] funksiya grafigi ZyZxE RxRyD ,)( ,)(