2-Kurs talabalari uchun "Oliy matematika" fanidan test topshiriqlari

208. 
     f(x)=2x²-lnx funksiyaning kamayish oralig’ini toping
     

A) *(0;0.5) B) (1;2) C) (2;e) D) funksiya har doim o’suvchi

209. 
     f(x)=e^x+5x funksiyaning o’sish oralig’ini toping
     

210. 
     Hosilani nolga aylantiruvchi nuqtalar qanday nomlanadi?
     

211. 
     Berilgan funksiyaning (a;b) oraliqdagi 2-tartibli hosilasi manfiy bo’lsa u holda funksiya grafigi…
     

212. 
     y=x⁵+5x-6 funksiyaning botiqlik oralig’ini va egilish nuqtasini toping
     

A) *(0;+∞) M(0;6) B) (1;2) M(0;6) C) (0;5) M(5;6) D) natural sonlar va (6;0)

213. 
     Tenglamalardan qaysilarini no’malum funksiyaga nisbatan differensiyal tenglama bo’ladi?
     

1) y 2x  0 ;	2) y 2 y  0;	3)	^2 y	 z 1 ;	4)		d ^2 y	50.
			x^2				dx^2
A) hammasi.	B)* 1,2,4		C) 3			D) 2.

214. 
     Funksiyalardan qaysilari ^dy_dx  y differensial tenglamaning yechimi bo’ladi?
     

1) y  3e^2 ^x ;	2) y  5e^x ;	3) y  e^x^^3 ;	4)	y 	x^2	 3.
				2
A) * 2),3) ;	B) hammasi.	C) 1),2),3) ;		D) 4.

215. 
     Tenglamalardan qaysilari 3-tartibli oddiy differensial tenglama bo’ladi?
     

1)

y



 2 y



0, 2)

d ^3 y

 y  0

,

3)





, 4)

^2 y

 y  0 .

dx^3

F ( y, y , y )  0

dx^2

A) *1,2,3

B) hammasi.

C) 1,2

D) 1.

216. Har bir nuqtasiga o’tkazilgan urinmaning burchak koeffitsiyenti Oy o’qidan shu nuqtagacha bo’lgan masofa yarmiga teng bo’lgan egri chiziq tenglamasini tuzing.

A)* 2 y x ; B) y 2x ; C) y  2x; D) x 2 y .

217. 
     Har bir nuqtasiga o’tkazilgan urunmaning burchak koeffitsiyenti shu nuqtaning absissasiga teng bo’lgan egri chiziq tenglamasini tuzing.
     

A)*	dy	 x ;	B)	dy	 y ;	C) y  x ;	D)	dx	 x .
	dx			dx				dy

218. 
     Har bir nuqtasiga o’tkazilgan urinmaning burchak koeffitsiyenti shu nuqta ordinatasining ikkilanganiga teng bo’lgan egri chiziq tenglamasini tuzing.
     

A) *	dy	 2 y ;	B) 2	dy	 y ;	C) 2 y  x ;	D)	dx	 2 y .
	dx			dx				dy

219. 
     Har bir nuqtasiga o’tkazilgan urinmaning burchak koeffitsiyenti koordinata boshidan shu nuqtasiga bo’lgan masofa teng bo’lgan egri chiziq tenglamasini tuzing.
     

dy

;B) y x^2  y^2 ;

C) y x  y ;

D)

dy

 x^2 .

A) *



x^2  y ^2

dx

dx

220. Tezligi v  t ^2

funksiya bilan berilgan jismning harakat qonunini yozing.

A) * s 

t ^3

 C ;

B) s  t ^2  C ;

C) S  2t ;

D) S  t ^3  3C .

3

221. 
     Tezligi v  t ³ qonuniyat bilan o’zgarayotgan jism 2 sekundda 3m masofa bosib o’tsa, uning harakat qonunini toping.
     

A) * s 

1

(t ^2  4) ;

B) s  t ^4 13;

C) s  t ^2 1;

D) s  t ^2  5 .

4

a 

6t funksiya bilan berilgan jismning harakat qonunini toping.

222. Tezlanishi

A)* s  t ^3

 C t  C

2

;

B) s  t ^3  C ;

C) s  3t ^2  C ;

D) s  6 .

1

223. Tezlanishi

a  t ^2

funksiya bilan berilgan jism tezligi qonuniyatini toping.

A) v 

t ^3

 C ;

B)

v  t ^2  C ;

C) * v 

t ^4

 C t  C

;

D) v  2t .

3

12

1

2