Toshkent davlat texnika universiteti "oliy matematika" kafedrasi
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54 – variant 1. 1 2 10 21 9 1 n 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
0 4 4 y y dy fdx 10.
2 2 2 2 , : 4 ,
4, 0
dxdydz V x y y y z z x y
11. . 0 , 3 ; 1 , 0 , 20 : ) ( : ) 2 7 ( 2 z xy z x y x y V dxdydz y x V
12. , 3 dl z y x I bu
yerda : t z t y t x , 3 , 2 3 2
chiziqning ) 0 ; 0 ; 0 ( A va
) 2 ; 3 2 2 ; 2 ( B nuqtalar orasidagi yoyi. 13.
ydx xdy I bu yerda :
2 ,
x x y parabolalar orasidagi egri chiziq yoyi.
32
1.
1 2 20 9 1
n n
2. 1 2 )! 2 ( 1
n n
3. 3 1 ln ln(ln ) n n n n
4. ∑ ( )
5. ∑ ( )
√
6. ( ) funksiyani ning darajalari bo‟yicha qatorga yoying. 7.
5 1,1,
0,00001 8. ( ) {
Ushbu funksiyani Fur‟е qаtоrigа yoying. 9. 2 3 1 0
dy fdx
10.
2 2 2 2 1, , 2 ,
, 2
y x y x z x y z x y
11. . 0 , 0 , 0 ; 1 4 8 15 : ) ( : ) 4 8 15 1 ( 2 z y x z y x V z y x dxdydz V
12. , 1 2 2 2
z y x I bu yerda :
2 ; 1 ( A va
) 6 ; 3 (
nuqtalarni tutashtiruvchi to„g„ri chiziq kesmasi. 13. ,
ydx xdy I bu yerda :
y t x 3 3 sin 4 , cos 4 astroida yoyi.
1.
1 2 6 35 49 1
n n
2. 1 )! 3 (
n n n
3. 3 1 ln(ln ) n n n
4. ∑ ( )
5. ∑ ( )
6. ( ) √
funksiyani ning darajalari bo‟yicha qatorga yoying. 7. 3
0,00001 8. ( ) {
Ushbu funksiyani Fur‟е qаtоrigа yoying. 9. 2 2 2 0 2 x x x dx fdy 10.
0, 0, 2 6
y x y z
11.
. 0 , 0 , 0 ; 1 , 3 : ) ( : 2 z y x z x y V dxdydz x V
12.
, ydl I bu yerda :
x x y 4 , 4 2 2
parabolalar orasidagi egri chiziq yoyi. 13.
, ) 1 (
y x ydy xdx I bu yerda :
1 ; 1 ; 1 ( A va
) 4 ; 3 ; 2 ( B nuqtalarni tutashtiruvchi to„g„ri chiziq.
33
1.
... 6 5 4 1 5 4 3 1 4 3 2 1 3 2 1 1
2. 1 3 ; 2 1 n n
3. 5 2 1 ln n n n
4. ∑ ( )
5. ∑ ( )
6.
( ) √ funksiyani Makloren qatoriga yoying. 7. 27 ,
0, 001 8. ( ) funksiyani ( dа Fur‟е qаtоrigа yoying. 9.
4 0 sin 0 2 4 cos
0 .
y fdx dy fdx dy 10.
1 2 0 0
( )
y dxdy 11.
. 0 , ; 1 , 0 , 4 : ) ( : ) 90 60 ( 2 2 z y x z x y x y V dxdydz z y V
12. AB y x dl I , 2 2 bu yerda AB-uchlari A(0;-2), B(4;0) nuqtalardan iborat kesma. 13.
, sin
cos AB xdy ydx I bu yerda AB- kesma: A(2;-2), B(-2;2).
1.
... 13 10 1 10 7 1 7 4 1 4 1 1 2.
1 1 ; 1 1 2 n n n
3. 6 2 1 ln n n n
4. ∑ ( )
( )
5. ∑ ( )
6. ( )
funksiyani ning darajalari bo‟yicha qatorga yoying. 7. 8 ,
0, 001 8. ( )
funksiyani dа Fur‟е qаtоrigа yoying. 9.
1 2 0 2 0 1 0 3
x fdy dx fdy dx
10. 2 1 2 0 x x xy dxdy
11.
. 0 , ; 1 , 0 , 9 : ) ( : ) 3 5 3 10 ( z xy z x y x y V dxdydz x V
12. ,
I
bu yerda -ushbu 2 , 4 , 0 , 0
x y x
to„g„ri chiziqlardan tashkil topgan to„rtburchak konturi. 13.
AB xydy dx y x I , ) ( 2 2 bu yerda AB- kesma: A(2;2), B(3;4).
34
1.
... 7 4 1 6 3 1 5 2 1 4 1 1 2.
1 3 3 ; 2 ! ! 3
n n n
3. 1 2 1 , ( 0) ln (ln ln ) n n n n
4. ∑ ( )
5. ∑ ( )
( )
6. ( ) funksiyani Makloren qatoriga yoying. 7.
24 , 0, 001
8. ( ) funksiyani dа kоsinuslаr bo‟yichа Fur‟е qаtоrigа yoying. 9.
1 0 0 1 1 ln .
e y fdx dy fdx dy 10.
1 1
y e y dxdy x
11. . 0 , ; 1 , 0 , 4 : ) ( : ) 18 9 (
xy z x y x y V dxdydz z V
12. , 4 2 2 y x dl I bu yerda - uchlari O(0;0), A(1;2) nuqtalardan iborat kesma. 13.
dy y x dx y x I , ) 4 ( ) 4 ( bu yerda B A yoy 4 x y egri chiziqning yoyi: A(1;1) va B(-1;1).
1.
... 8 1 3 2 4 1 3 2 2 1 3 2 3 2
2. 1 ; 1 2 n n n
3. 2 2 1 ln (ln ln ) n n n n
4. ∑ ( )
5. ∑
( )
6. ( ) funksiyani ning darajalari bo‟yicha qatorga yoying. 7. 0,3,
0, 0001 sh 8. ( ) funksiyani ( yarim intеrvаldа Fur‟е qаtоrigа yoying. 9.
1 0 0 2 1 0 2 . y y fdx dy fdx dy
10. 1 3 2 1
ln ( 3) x y dxdy y x 11.
. 0 , 0 , 0 ; 1 3 , 15 : ) ( : 25 2
y x z y x V dxdydz y V
3. 12. , ) ( dl z x I bu yerda egri chiziq parametrik tenglamalari bilan berilgan: . 2 1 0 , 2 ), 1 ln( , 1 2 2 2 2 t at z t a y t at x 13.
, B A xdy ydx I bu yerda B A yoy 1 2 2
x aylananing ) 2
; 2 1 ( A
nuqtasidan ) 2 1 ; 2 1 ( B nuqtasigacha soat millari harakati yo„nalishida o„tiladi.
35
1. Claudio Canuto, Anita Tabacco. Mathematical Analysis I, II. Springer-Verlag Italia, Milan 2015, 2010. 2. Soatov Yo.U Oliy matematika. T., O„qituvchi, 1995. 1- 3 qismlar. 3. Д.Писменный. «Конспект лекции по высшей математике», 1,2,3 часть. -M.: Айрис Пресс, 2008.
4. Ю.Ф. Сенчук. Математический анализ для инженеров. 1,2 часть-Харков: НТУ «ХПИ», 2003.- 408 с.
5. Axmedov A.B., Shodmonov G., Esonov E.E., Abdukarimov A.A., SHamsiyev D.N. Oliy matematikadan individual topshririqlar. –Toshkent: O‟zbekiston ensiklopediyasi, 2014. 6. Xurramov SH. R. Oliy matematika.1,2-qism. – Toshkent: “Tafakkur” nashriyoti, 2018. 7. Xolmurodov E., Yusupov A.I., Aliqulov T.A. Oliy matematika. 1,2,3-qismlar. –Toshkent: “NEXT MEDIA GROUP”, 2017. 8. John James Stewart. Calculus.Seventh editions. Metric version. Brooks/Cole, Cengage Learning, 2012. 9. Y. Suhov, M. Kelbert. Probability and Statistics by Example. 2nd edition. United Kingdom. University printing house, Cambridge CB2 8BS, 2014. 10. В.Е.Шнейдер, А.И.Слуцкий, А.С. Шумов, Краткий курс высшей математики. -М.:, 1978., 1, 2-части. 11. П.Минорский. Сборник задач по высшей математике. ФИЗМАТЛИТ 2010й. 12. А.П.Рябушко и др. Сборник задач индивидуальный заданий по высшей математике. 1, 2-части. – Минск: высшая школа, 1991. Internet saytlari: 1. www. ziyonet.uz; 2. www. gaap.ru; 3. www. cip.com; 4. www. aicpa.ord; 5.
www.bilim.uz ;
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