Namuna test
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NAMUNA TEST
x x dx integralni hisoblang 5 3
2 2( 3) ( 3) 5 x x C
5 2 2( 3) 5 x C 3 2 ( 3)
C 5 3 2 2 ( 3) 5
x C
98. 2 3 sin x x dx
integralni hisoblang 3 1 cos( ) 3 x C 3 cos( ) x C
3 1 3 x C 1 3 C
99.
4 1 ( ) х dx х integralni toping. 5 ln 5 x x C 5 5 1 5
C x 5 2 5 2
x C 5 5 x C
100. 20 (2 1) х dx integralni toping. 21 (2
42 x
21 (2 1) 21 x
2 1 2 x
19 (2 1) 10 x
101. 2 sin cos x xdx
integralni toping. 3 sin 3 x
3 2 sin
cos 3 2 x x
2sin cos x x
2 2 sin cos x x
102. ? dx x ln x C
sin x C
x e C
cos x C 103.
2 ?
e dx 2 1 2 x e C
sin x C
ln x C
cos x C 104.Integralni toping. x xe dx
( 1)
e x c
( 1) x e x c
x e x c
x e x c
105.Integralni toping. 2
tgx x
tgx x
tgx x
tgx x
106.Quyidagi integrallarning qaysi biri 3
ln 3 2 2 4 x x
ga teng. 2 3 2 1 x dx x
2 3 2 1 x dx x
2 3 2 1 x dx x
2 1 1
dx x
107.Hisoblang: 3 3 1 1 x dx
24 4 –20
19 108.Hisoblang: 4 1
2 3 4 1 109.Hisoblang: 1 0 ( 1)
dx 1 2
3 2
2 3
1 110.Hisoblang: sin
a a x dx 0 2sin a
1 2sin a
111.Hisoblang: 1 0
-0,5 1 -1 112.Hisoblang: 3 2 0 х dx
9 -3
27 81
113.Hisoblang: 3 2 2х dx 5 8 7 6 114. 2 1 ln xdx integralni hisoblang` 2ln2-1
ln2-1 ln2+1
ln2+2 115.
1 2 1 dx x integralni hisoblang -2 -1
2 0 116. 0 1 ( 1) х dx
integralni hisoblang 1 2
2 sin
2 x
1 2 0
117.Hisoblang: 3 3 1 1 x dx
24 4 –20
19 118.Hisoblang: 4 1
2 3 4 1 119.Hisoblang: 1 0 ( 1)
dx 1 2
3 2
2 3
1 120.Hisoblang: sin
0 2sin a
1 2sin a
121.Hisoblang: 1 0
-0,5 1 -1 122.Hisoblang: 3 2 0 х dx
9 -3
27 81
123.Hisoblang: 3 2 2х dx 5 8 7 6
124. 2 1 ln xdx integralni hisoblang` 2ln2-1
ln2-1 ln2+1
ln2+2 125.
1 2 1 dx x integralni hisoblang -2 -1
2 0 126. 0 1 ( 1) х dx
integralni hisoblang 1 2
2 sin
2 x
1 2 0 127. 2 0 sin 2x dx ni xisoblang? 1 3 2 0.5
128.Kuyidagi xosmas integralni xisoblang? 0
2 x e dx 0.5 1 1.5 2 129.
0 !
n x n qator qaysi funksiyaning yoyilmasi bo`ladi? x e
cos x sin x
130. 1 1 1 1 ...
... 1 2
2 3 3 4
1 n n qatorning yig’indisini to‘ing
1 2 0 4 131.
2 3 1! 2! 3! ! ... ...
1 2 3 n n n
qatorning yaqinlashishga tekshiring Yaqinlashuvchi Uzoqlashuvchi 1;1 oraliqda yaqinlashuvchi ; e e oraliqda yaqinlashuvchi 132.
2 2 1 1 1 1 1 1 ... ... 2 3 2 3 2 3 n n
qatorning yig’indisini to‘ing 3/2
1/3 0 1 13. 2 3 1 3 5 2 1 ... ... 2 2 2 2
n
3 2 1 1/2
qatorning yig’indisini to‘ing
133. 4 2 1 n x n qatorning yaqinlashish sohasini to‘ing
| | 1 x
| | 1 x
1 x
x R
134. 1
n nx e qatorning yaqinlashish sohasini to‘ing
0 x
0 x
0 x
x R
135. 4 3 1 4 3 n n x n qatorning yig’indisini to‘ing 1 1
ln 2 4 1 x arctgx x
1 1 1 ln 2 4 1 x arctgx x
1 1 1 ln 2 4 1 x arctgx x
1 1 1 ln 2 4 1 x arctgx x
136. 2 x y e funksiyani qatorga yoying
2 1 2 2 1 2
... ...
2! 1 !
n x x x n
2 1 2 2 1 2 ...
1 ...
2! 1 !
n n x x x n
2 ...
... 2! ! n x x x n
2 1 ...
... 2! ! n x x n
137.Garmonik qatorni ko‘rsating 1 1 n n
2 1 2
n
1 1 1 1 n n n 1 0 n n aq
138.Koshining radikal alomatini tatbiq qilish uchun qaysi limitnidan foydalanish kerak lim
1 lim (1
) n n n a n a
1 lim n n n a a
1 lim
x x f t dt 139.Dalamber alomatini tatbiq qilish uchun qaysi limitnidan foydalanish kerak 1 lim n n n a a 1 lim (1 ) n n n a n a
lim n n n a
1 lim x x f t dt 140.Koshining radikal alomatini tatbiq qilish uchun qaysi limitnidan foydalanish kerak
1 lim
x x f t dt 1 lim (1 ) n n n a n a
lim n n n a
1 lim
n n n a a 141.Raabe alomatini tatbiq qilish uchun qaysi limitnidan foydalanish kerak 1 lim (1 ) n n n a n a
1 lim
x x f t dt lim
n n n a
1 lim
n n n a a 142.
2 x y e funksiyani qatorga yoying
2 1 2 2 1 2
... ...
2! 1 !
n x x x n
2 1 2 2 1 2 ...
1 ...
2! 1 !
n n x x x n
2 ...
... 2! ! n x x x n
2 1 ...
... 2! ! n x x n
143.
2 4 2 1 1 ... 1 ...
2! 4! 2 ! n n x x x n
qator qaysi funksiyaning qatorga yoyilmasi? cos x
sin x tgx
e
144. 2 1 4 1 2 1 ... 1 ...
2! 1 !
n n x x x n qator qaysi funksiyaning qatorga yoyilmasi? 2
2 x e
sin x cos x
145.
ln cos y x
funksiyani 0
nuqta atrofida qatorga yoyib dastlabki beshta hadini yozing. 2 4 ... 2 12 x x 2 1 ... 2
x
4 2 ...
4 x x 2 4 6 8 ... x x x x
146. dy x dx
tenglamaning umumiy yechimini toping. 2 2
y C 2 2 2 x y C 3 2 x y C 3 7 2 x y C 147.
1 dy dx
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