+ bx +c funksiyaning grafigi koordinatalar tekisligining qaysi choraklarida joylashadi ?

1. Agar a > 0 va b ² - 4ac < 0 bo`lsa, y = ax ² + bx +c funksiyaning grafigi koordinatalar tekisligining qaysi choraklarida joylashadi ?
A) I, IV B) I, II, IV C) IV D) III, IV E) I,II
2. Tengsizlikni yeching: (x – 2) (x+3) > 0.
A) (-∞;2) U (3;∞) B) (-∞;-3) U (2;∞) C) (-∞;-2) U (3;∞) D) (-∞; ∞)
3. Ushbu (y +6) (y +2) < 0 tengsizlikning barcha butun yechimlari yig`indisini toping.
A) 12 B) 20 C) -12 D) -20 E) -9
4. Tengsizlikning butun yechimlari ko`paytmasini toping: 2x ² – 9x + 4 <0
A) 0 B) 4 C) 24 D) 8 E) 6
5. Tengsizlikni yeching: (x – 2) ² + 3 (x – 2) ≥ 7 – x
A) [0;1] U [3;∞) B) [-2;1] C) [-3;3] D) [3;∞ ) E) (-∞;-3] U [3; ∞)
6. Agar f(x) = 5sinx + 3 cosx bo`lsa, f ' ( ) ni hisoblang.
A) - B) C) -2 D) 4 E) 4
7. Ushbu y = 6 ^x -6 funksiyaning x = 1 nuqtadagi hosilasini toping.
A) ln12 B) ln36 C) ln 6 D) ln E) 6
8. y = (x-3)(x² + 3x + 9) funksiyaning x = 3 nuqtadagi hosilasini aniqlang.
A) 0 B) 3 C) 27 D) -27 E) 9
9. Nechta nuqtada f(x) = x ³ funksiya va uning hosilasi qiymatlari teng bo`ladi.
A) 2 B) 1 C) 0 D) 3 E) 4
10. f(x) = ׀ x² – 14x + 45 ׀ . f ' (9) = ?
A) 0 B) 4 C) 2 D) 7 E) mavjud emas.
11. Agar f(x) = x ³lnx bo`lsa , x f '(x) = 2f(x) tenglamani yeching.
A) B) e C) D) 2e E) 1
12. f(x) = . f ' (-2) = ?
A) -1 B) -2 C) 1 D) 2 E) 4
13. Ushbu f(x) = ln(x² – 3 sinx ) funksiyaning hosilasini toping.
A) B) C) D) E)
14. f(x) = bo`lsa , f ' ( ) = ?
A) 1 B) C) D) E)
15. Quyidagi funksiyalardan qaysi biri (0; ∞ )oraliqda kamayuvchi bo`ladi ?
A) y = x +8 B) y = 3 – x C) y = - D) y = 2x ² E) y =
16. y = -x ² + 2x – 1 funksiyaning o`sish oralig`ini toping.
A) (1;∞ ) B) (0;∞ ) C) (-∞; -1 ) D) ( -1; ∞) E) (-∞;1]
17. f(x) = -2x ³ + 15x ² +12 funksiya o`sadigan kesmaning uzunligini toping.
A) 5 B) 4 C) 6 D) 4,5 E) aniqlab bo`lmaydi.
18. Ushbu f(x) = 3x – x³ funksiyaning maksimumini toping.
A) -1 B) 2 C) -2 D) 4 E) maksimumi yo`q
14. Ushbu f(x) = 3 ^{1+ x} + 3 ^{1 – x} funksiyaning eng kichik qiymatini toping.
A) 9 B) 4 C) 8 D) 6 E) 5
19. Ikki tomoni yig`indisi 1,6 ga va ular orasidagi burchagi 150 <sup>º</sup> ga teng bo`lgan uchburchaklar ichida yuzasi eng katta bo`lgan uchburchakning yuzini toping.
A) B) C) D) E)
20. y = 4x ² + funksiyaning [ ;1] kesmadagi eng katta va eng kichik qiymatlari yig`indisini toping.
A) B) C) D) 6 E) 8
21. y = lnx + x ² funksiyaning grafigiga x₀ = nuqtada o`tkazilgan urinmaning burchak koeffitsiyentini toping.
A) 3 B) 6 C) 4 D) 6,5 E) 3,5
22. Qaysi nuqtada y = x ³ – 2x² +4 va y = x ³ – lnx funksiyalarning grafiklariga o`tkazilgan urinmalar o`zaro parallel bo`ladi ?
A) x = B) x = C) x = 2 D) x = - E) x = 3
23. y = 1 – 2x ² funksiya grafigiga abssissasi x₀ = 0 nuqtada o`tkazilgan urinmaning tenglamasini ko`rsating.
A) y =1 B) y = -1 C) y = - x D) y = 1 – 4x E) y = 2x-1
24. y = x ² – 2x parabolaga uning biror nuqtasida o`tkazilgan urinmaning burchak koeffitsiyenti 4 ga teng. Shu urinmaning tenglamasini toping.
A) y = 4x – 4 B) y = 4x +9 C) y = 4x + 4 D) y = 4x – 5 E) y = 4x – 9
25. To`g`ri chiziq bo`ylab x(t) = - t <sup>3</sup> + 3t <sup>2</sup> +9t qonun bo`yicha harakatlanayotgan moddiy nuqta harakat boshlangandan necha sekunddan keyin to`xtaydi ?
A) 1 B) 2 C)3 D) 4 E) 5
26. ushbu s(t) = 4t ² - qonuniyat bilan harakatlanayotgan jismning eng katta tezligini aniqlang.
A) 16 B) 20 C) 12 D) 24 E) 36
27. Ushbu f(x) = 1 - funksiyaning boshlang`ich funksiyasining umumiy ko`rinishini toping.
A) x + ctgx + c B) x - tgx + c C) x - tg3x + c D) tg3x + c E) x - ctg3x + c
28. F(x) = lncosx + c funksiya quyidagi funksiyalardan qaysi birining boshlang`ich funksiyasi bo`ladi ?
1) y = -ctgx 2) y = ctgx 3) y = tgx 4) y = -tgx
A) 1 B) 2 C) 3 D) 4 E) hech qaysisining boshlang`ich funksiyasi bo`lmaydi.
29. Agar f '(x) = 6x ² – 3x +5 va f(4) = 130 bo`lsa, f(0) = ?
A) 6 B) 4 C) -4 D) -6 E) 8
30. Ikkita o`xshash uchburchaklarning perimetrlari 18 va 36 ga, yuzlarining yig`indisi 30 ga teng. Katta uchburchakning yuzini toping.
A) 20 B) 24 C) 21 D) 18 E) 25