Toshkent davlat texnika universiteti "oliy matematika" kafedrasi
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3-TIPIK HISOB (1)
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- 20 – variant
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- 24 – variant
- 25 – variant
- 26 – variant
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10.
2 2 , : 1, , 2 D x dxdy D xy y x x y
11. . 0 , 0 , 0 ; 1 ), 3 ( 10 : ) ( : 2
y x x y y x z V dxdydz y V
12. , 2 2 dl y x I buyerda
:
y x 4 2 2 aylanayoyi. 13.
, 1 1 1 dz x dy z dx y I buyerda
: ) 1 ; 1 ; 1 ( A va ) 8 ; 4 ; 2 ( B dano„tganto„g„richiziqkesmasi.
1. 1 2 4 1 n n n
2. 1 2 2 2 1 1 2 n n n n
3. 2 2 2 1 ln
n n
4. ∑ ( )
√
5. ∑ ( )
6. ( )
funksiyani ning darajalari bo‟yicha qatorga yoying. 7. 0, 3, 0, 0001 cth 8. ( )
funksiyani dа Fur‟е qаtоrigа yoying. 9. 2 2 1 2 4 x dx fdy 10.
, : 0, 2, 1,
x D e ydxdy D x x y y e 11.
. 0 , 15 ; 1 , 0 , : ) ( : ) 2 3 5 ( 2 2
y x z x y x y V dxdydz z x V
12. ,
I buyerda
: 12 4 3 y x to„g„richiziqningkoordinatao„qlariorasidagikesmasi. 13. ,
dz e dy e dx e I y x x z z y buyerda
: ) 0 ; 0 ; 0 ( O bilan
) 5 ; 3 ; 1 ( A nibirlashtiruvchikesma.
15
21 – variant 1.
1 2 3 4 1 n n n
2. 1 2 2 3 1 2
n n n
3. 2 3 2 1 ln
n n
4. ∑ ( )
5. ∑ ( )
6. ( )
funksiyani
atrofida Teylor qatoriga yoying. 7. arcsin 0, 4, 0, 0001 8. ( ) funksiyani ( ) intеrvаldа Fur‟е qаtоrigа yoying. 9. 1 2 0 2 x x dx fdy 10.
2 2 2 ( ) , : 0, 1, 0, D x y dxdy D x x y y x
11.
. 0 , 0 , 0 ; 1 5 3 8 : ) ( : ) 5 3 8 1 ( 2 z y x z y x V z y x dxdydz V
12. , xydl I buyerda
: 12 3 4 y x to„g„richiziqningkoordinatao„qlariorasidagikesmasi. 13. ,
( ) 2 ( ) (
y x dy x dx z y I buyerda
- yoy: 25 2 2 2 z y x sferadagi ) 0
4 ; 3 ( M bilan
) 5 ; 0 ; 0 ( A nibirlashtiruvchikattaaylananingengqisqayoyi.
1.
1 2 12 1 n n n
2. 1 1 2 n n n n
3. 1 1 1 n n
4. ∑ ( )
5. ∑
( )
6. ( ) ( )funksiyani Makloren qatoriga yoying. 7. arcsin 0, 6, 0, 0001 8. ( ) {
Ushbu funksiyani Fur‟е qаtоrigа yoying. 9. 2 4 12 0 3 x x dx fdy
10.
, : 0, 0, 3, 0, 2 V xdxdydz V x y y z x z
11. . 0 , 0 , 0 ; 1 5 3 , 8 : ) ( : 10 2 z y x z x y V dxdydz x V
12. , ) ( dl y x xy I buyerda
: 2 2 2
y x aylananingyuqoriyoyi. 13.
,
dx x y I buyerda
:
y ln egrichiziqning ) 1 ; 0 ( A va ) 1 ; (e B nuqtalarorasidagiyoyi.
16
23 – variant 1.
1 2 2 3 9 1
n n
2. 2 1 5 10 n n n n
3. 1 1 3 4
n
4. ∑ ( )
√
5. ∑ ( )
( )
6. ( )
funksiyani ning darajalari bo‟yicha qatorga yoying. 7. arcsin 0, 9, 0, 0001 8. ( ) , . ( ) funksiyani kеsmаdа juft dаvоm ettirib Fur‟е qаtоrigа yoying. 9. sin
2 0 0 x dx fdy 10.
, : 0, 0, 0, 1 V xyzdxdydz V x y z x z y
11. . 0 , 0 , 0 ; 1 2 , 3 : ) ( : ) ( 25 2 z y x y x y x z V dxdydz x y V
12. , 4 2 2 dl y x I buyerda
: ) cos 1 ( a r kardioidayoyi. 13. ,
2 ( dy e dx x ye I x x buyerda
: 2 xe y egrichiziqning ) 0 ; 0 (
va )
1 ( e B nuqtalarorasidagiyoyi.
24 – variant 1.
1 2 20 9 9 1
n n
2. 1 )! 1 ( 3 1 2 n n n n
3. 4 3 1 n n n e
4. ∑ ( )
5.∑
( )
6. ( ) √
funksiyani Makloren qatoriga yoying. 7. arccos 0, 4, 0, 0001 8. ( ) { , . ( ) funksiyani kеsmаdа juft dаvоm ettirib Fur‟е qаtоrigа yoying. 9. 2
2 0
x dx fdy 10.
2 2 2 2 ( ) , : 2, 2 V x y x y dxdydz V z z 11.
. 0 , 0 , 0 ; 1 8 2 3 : ) ( : 8 2 3 1 z y x z y x V z y x dxdydz V
12. , 2
y I
bu yerda : ) cos
1 ( , ) sin
( t a y t t a x , ) 2 0 ( t
sikloidaning bir arkasi. 13. , 2 2
x dx y I buyerda
: 1 2 2 2 2 b y a x ellipsning ) ;
( b A va ) 0 ; (a B nuqtalarorasidagiyoyi.
17
25 – variant 1.
1 2 3 4 4 1
n n
2. 1 2 2 2 ) ! ( n n n
3. 5 4 1 n n n e
4. ∑
5. ∑ ( )
( )
6. ( ) ( ) funksiyani
nuqta atrofida Teylor qatoriga yoying. 7. arccos 0, 3, 0, 0001 8. ( ) funksiyani ( ) intеrvаldа Fur‟е qаtоrigа yoying. 9. 2 3 2 0 2 x x x dx fdy 10.
2 2 2 2 2 ( ) , : , 0, 2 V x y dxdydz V x y x z z x 11.
. 0 ), 2 ( 3 ; 1 , 0 , 6 : ) ( : 4 2 2
y x z x y x y V xydxdydz V
12. , ) ( 2 2 2
z y x I buyerda
: 2 0 , 3 , sin
, cos
t z t y t x vintchizig„iningbirinchio„rami. 13. ,
ydx xdy I buyerda
: 2 2 2
y x aylananingyoyi.
26 – variant 1.
1 2 10 21 9 1
n n
2. 1 )! 1 2 ( ! 10 n n n n
3. 3 2 1 n n n e
4. ∑ ( )
5.∑
( )
√
6. ( ) funksiyani ning darajalari bo‟yicha qatorga yoying. 7. arc 3, 0, 0001
tg 8.
( )
funksiyani ( ) intеrvаldа Fur‟е qаtоrigа yoying. 9. 3 8 1 0 4 4
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