LISTA FÓRMULAS CALCULO TUDO calculo 1 e 2

Prévia do material em texto

I – TRIGONOMETRIA
Identidades Fundamentais:
 1.1. cotg x =
; sec x =
; cossec x =
 1.2. tg x =
; cotg x =
 
 1.3. sen2x + cos2x = 1 
 1+ tg2x = sec2x 
 1+ cotg2x = cossec2x 
2. Fórmulas de Redução:
 2.1. sen(
/2 
 x) = cos x
 cos(
/2 
 x) = 
 sen x
 tg(
/2 
 x) = 
 cotg x
 2.2. sen(
 x) = 
 sen x
 cos(
 x) = 
 tg(
 x) = 
 tg x
 2.3. sen(2
 x) = 
 sen x
 cos(2
 x) = cos x
 tg(2
 x) = 
 tg x
 Função da Soma e Diferença de 2 Ângulos:
3.1. sen(x
y) = sen x . cos y 
 sen y . cos x
 3.2. cos(x
y) = cos x . cos y 
 sen x . sen y
 3.3 tg(x
y) =
Fórmulas de Fatoração:
4.1. sen x + sen y = 2 . sen
 . cos
 4.2. sen x – sen y = 2 . cos
 . sen
 4.3. cos x + cos y = 2 . cos
 . cos
 4.4. cos x – cos y = 
 sen
 . sen
 4.5. 
 tg y = 
Relação entre as funções de x e 2x
5.1. sen 2x = 2 . sen x . cos x
 5.2. cos 2x = cos2x – sen2x = 2.cos2x – 1= 1 – 2.sen2x
 5.3. sen2x = ½ . (1 – cos 2x)
 5.4. cos2x = ½ . (1 + cos 2x)
 5.5. tg 2x = 
Expressões para qualquer Triângulo
 6.1. Lei do cosseno: a2 = b2 + c2 – 2bc.cos Â
 6.2. Lei do seno: 
 6.3. Área: ½ bc . sen  
	Rad
	0
	
	
	
	
	
	
	Grau
	0o
	30o
	45o
	60o
	90o
	180o
	270o
	Sen
	0
	
	
	
	1
	0
	-1
	Cos
	1
	
	
	
	0
	-1
	0
	Tg
	0
	
	1
	
	
	0
	
	Cotg
	
	
	1
	
	0
	
	0
	Sec
	1
	
	
	2
	
	-1
	
	Cosec
	
	2
	
	
	1
	
	-1
 II – ÁLGEBRA
Fórmula Binomial:
 (x + y)n = xn + n . xn – 1. y + 
 + 
 + 
 + 
+ 
 onde n é um nº positivo e n! (n fatorial) é 
 n! = n . (n – 1) . (n – 2) . . . 2 . 1
Produtos Especiais:
2.1 (x + y)2 = x2 + 2xy + y2 
2.2 (x – y)2 = x2 – 2xy + y2 
 2.3 (x + y)3 = x3 + 3x2y + 3xy2 + y3
 2.4 (x – y)3 = x3 – 3x2y + 3xy2 – y3
 2.5 x2 – y2 = (x – y) (x + y) 
 2.6 x3 – y3 = (x – y) (x2 + xy + y2) 
 2.7 x3 + y3 = (x + y) (x2 – xy + y2) 
 2.8. 
 
Equação do 2º Grau:
 As raízes da equação do 2º grau ax2 + bx + c = 0,
 são determinadas por:
 
 onde 
 Se 
 < 0 
 raízes imaginárias
 Se 
 = 0 
 raízes iguais
 Se 
 > 0 
 raízes reais e diferentes
 Se x1 e x2 são raízes então: x1+x2 =
 e x1.x2 =
 Abscissa do vértice da parábola:
 ou 
Propriedades da Potenciação e Radiciação:
 4.1. ap.aq = ap + q 	 4.2. 
 = ap – q 
 4.3. (ap)q = ap . q 	 4.4. a0 = 1, a  0
 4.5. a – p = 
	 4.6. (a . b)p = ap . bp
 4.7.
 4.8. 
 
 4.9. 
�� EMBED 4.10. 
 4.11. 
 4.12. 
Logarítmo:
 Se N = ax, onde a é um número positivo diferente de 1, então x = logaN, é chamado logarítmo de N na base a, onde N > 0.
6. Propriedades dos Logarítmos:	
6.1. logaM.N = logaM + logaN
6.2. loga
= logaM – logaN
6.3. logaa = 1 
6.4. logaNn = n . logaN
6.5. loga
= – logaN
6.6. loga1 = 0
6.7. 
6.8. logba = 
6.9. logbN = logaN . logba = 
6.10. logaaN = N . logaa = N
6.11. ln eN = eln N = N
III – DERIVADAS
Seja u, v, w 
 funções de uma variável x.
Seja a, k, m, n 
 constantes.
As derivadas de u, v, w em relação a x serão:
 1. D(u 
 v 
 w) = Du 
 Dv 
 Dw 
 2. D(k) = 0 
 3. D(x) = 1 
 4. D(kx) = k 
 5. D(k.xn) = n.k.xn-1 
 6. D(k.u) = k.Du 
 7. D(u.v) = u.Dv + v.Du 
 8. D(u.v.w) = v.w.Du + u.w.Dv + u.v.Dw 
 9. D
 
10. D
11. D
�� EMBED 
12. D(um) = m.um-1.Du
13. D
14. D(au) = au.ln a. Du 
15. D(eu) = eu. Du 
16. D(vu) = vu. ln v. Du + u.vu-1. Dv (exponencial geral) 
17. D(logau) = 
 
18. D(ln u) = 
 
19. 
 (Regra da Cadeia)
20. 
 (Derivada da Função Inversa) 
21. D(sen u) = (cos u). Du 
22. D(cos u) = ( – sen u). Du 
23. D(tg u) = (sec2 u). Du 
24. D(cotg u) = ( – cossec2 u). Du
25. D(sec u) = (sec u . tg u). Du 
26. D(cossec u) = ( – cossec u . cotg u). Du 
27. D(arc sen u ) = 
 ou D(sen– 1 u) 
28. D(arc cos u) = 
 ou D(cos– 1 u) 
29. D(arc tg u) = 
 ou D(tg– 1 u) 
30. D(arc cotg u) = 
 ou D(cotg– 1 u) 
31. D(arc sec u) =
 ou D(sec– 1 u) 
32. D(arc cossec u) = 
 ou D(cossec– 1 u) 
33. D(senh u) = (cosh u). Du
34. D(cosh u) = (senh u). Du
35. D(tgh u) = (sech² u). Du
36. D(cotgh u) = ( – cosech² u). Du
37. D(sech u) = ( – sech u. tgh u). Du
38. D(cosech u) = ( – cosech u. cotgh u). Du 
IV – DIFERENCIAIS
As regras para diferenciais são análogas às das derivadas, já que “diferencial de uma função y = f(x) é igual à derivada da função multiplicada pela diferencial da variável independente”, e obtemos:
dy = Df(x).dx ou dy = f ’(x).dx
V – INTEGRAIS IMEDIATAS 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
10. 
 
11. 
 
12. 
 
13. 
 
14. 
 
15. 
 
16. 
 
17. 
 
18. 
 ou = 
 
19. 
 
20. 
21. 
 ou =
 
22. 
 23.
 ou = 
 
24.
25. Integração por partes
 
Organizado por: Profº Ms.: Sérgio Silva de Sousa, pfsergiosousa@yahoo.com.br. Bibliografia: Cálculo: Anton, Boyce, Leithold,, Stewart, Swokowski
Organizado por: Profº Ms.: Sérgio Silva de Sousa, pfsergiosousa@yahoo.com.br. Bibliografia: Cálculo: Anton, Boyce, Leithold,, Stewart,
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