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Тригонометрия

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1. sin²x + cos²x = 1 6. sin 2x = 2sin x*cos x 11. cos²x = 22.sinx ± siny = 26.

2. tg x*ctg x = 1 7. cos 2x = cos²x – sin²x 12. sin²x = 23. cos x + cos y = 27.

3. 1 + tg²x = 8. cos 2x = 2cos² - 1 13.cos³x = 24. cos x - cos y = 28.

4. 1 + ctg²x = 9. cos 2x = 1 – sin²x 14. sin³x = 25. tgx ± tgy =

5. tg x + ctg x = 10. tg 2x = 29. sin 3x = 3 sin x – 4 sin³x 30. cos 3x = 4 cos³x – 3 cos x

15. sin(x ± y) = sin x*cos y ± cos x *siny 19. sinx* siny = 31. 32.

16. cos(x + y) = cos x*cosy - sinx*siny 20. cosx*cosy = 1. sin x = 0, x = πn. 1. cos x = 0, x = + πn.

17. cos(x - y) = cos x*cosy + sinx*siny 2. sin x = 1, x = + 2 πn. 2. cos x = 1, x = 2 πn.

18. tg(x ± y) = 21. sinx*cosy = 3. sin x = -1, x = - + 2 πn. 3. cos x = -1, x = π + 2 πn.

4. sin x = a, x = (-1)ⁿarcsin a + πn 4. cos x = a, x = ± arcos a + 2 πn

Квадратное уравнение: ax² + bx + c = 0 ax² + bx + c = a(x – x₁)(x – x₂) 1. tg x = 0, x = πn. 2. tg x = ± 1, x = ± + πn.

D = X_1,2 = 3. tg x = a, x = arctg a + πn.

Теорема Виета: x² + px + q = 0; x₁ + x₂ = - p; x₁. x₂ = q.

Правила дифференцирования Правила интегрирования Логарифмы

(u + v)^/ = u ^/ + v ^/ (ku)^/ = ku^/ 1. dx = x 8. ò 1. a^log_a^b = b 2. log_a a = 1, a¹ 1, a > 0

(uv)^/ = u ^/v + uv ^/ 2. xⁿdx = 9. ò 3. log_a 1 = 0 4. log_abc = log_a b + log_ac

(f(kx + m))^/ = kf ^/(kx + m) 3. = ln | x | 10. ò 5. log_a = log_ab – log_a c

1. C¢ = 0 2. (kx + b)¢= k 3. (e^x)¢ = e^x 4. a^x dx = 11. ò 6. log_a b^p = p log_ab 7. log_ab =

4. (xⁿ)¢ = nx^{n - 1} 5. (a^x)¢ = a^x ln a 5. ò = tgx 12. ò 8. log_a b = 9.

6. (sin x)¢ = cos x 7. (cos x)¢ = -sin x 6. ò = -ctgx 13. ò cosx dx = sinx 10. log_ax^p = plog_a | x | p – чет.

8. (tg x)¢ = 9. (ctg x)¢ = - 7. ò e^x dx = e^x 14. ò sin x dx = -cosx 11. log_ab = x Û a^x = b

10.(ln x)¢ = 11. (log_ax)¢ = Свойства степени. ФСУ

12. ( ) = 13. (arctg x)¢ = 1. a⁰ = 1 (a¹0) 2. a¹ = a 3. a^r × a^s = a^{r + s} 1. a² – b² = (a – b)(a + b)

14. (arcsin x)¢ = 4. a^r: a^s = a^{r – s} 5. (a^r)^s = a^rs 6. a^r × b^r = (ab)^r 2. (a + b)² = a² + 2ab + b²

15. (arccos x)¢ = - 7. 8. a^-r = 9. 3. (a - b)² = a² - 2ab + b²

16. (arcctg x)¢ = - 10. если 0 < a < b, то 11. если r > s, то 4. a³ – b³ = (a – b)(a² + ab + b²)

17. Уравнение касательной: a^r > b^r при r > 0 a^r > a^s при a > 1 5. a³ + b³ = (a + b)(a² - ab + b²)

y = f(a) + f ^/(a)(x – a) a^r < b^r при r < 0 a^r < a^s при 0 < a < 1 6. (a + b)³ = a³ + 3a² b + 3ab² + b³

7. (a - b)³ = a³ - 3a² b + 3ab² - b³

Свойства корней Арифметическая прогрессии Геометрическая Симметрические системы

1. 2. 1. a_n = a₁ + d(n – 1). 1. b_n = b₁q^{n - 1} 1. х + у = u, xy = v 2. x² + у² = u² – 2v

3. 4. 2. S_n = = 2. S_n = = 3. x³ + y³ = u³ – 3uv 4. x⁴ + y⁴ = u⁴ – 4u²v + 2v²

5. 6. 3. a_n = 3. b_n = 5. x⁵ + y⁵ = u⁵ – 5u³v + 5uv³

Дата добавления: 2015-09-29