- PROBABILIDADES

Conhece a Matemtica e dominars o Mundo. Galileu Galilei_________________________________________________________________________________________________________________________________________

- PROBABILIDADES Prop. Distributiva: ;

Leis de De Morgan: ; Prob. Condicionada (acontecer A sabendo que B aconteceu): Lei Laplace: Acont. Independ.: ; .

Acont. Diferena( A realiza-se sem que B se realize ): ;

Permutaes Arranjos (a ordem importa) : s/ repetio c/ repetio

Combinaes (no h repetio e ordem no importa):

Binmio Newton

Prop. Tringulo Pascal:

Dist. Prob. : valor mdio varincia desvio padro

Coef. Binomial ( n=n experincias e r=n sucessos )

Estandardizao da varivel

- FUNES -

EMBED Equation.3

Assimpt. funo racional

Assimpt. Vert. Assimpt. Horiz.

Assimpt. Obliq.

Taxa variao mdia Definio derivada ou

Regras Derivao :

Alguns exemplos: Der. Composta:

- TRIGONOMETRIA -

Redues ao 1 quadrante:

Equaes trigonomtricas:

Circulo trigonomtrico:

- NMEROS COMPLEXOS -Forma algbrica n complexo: Conjugado de z: Mdulo de z: Argumento de z:

Forma trigonomtrica: ou

EMBED Equation.3

EMBED Equation.3

Operaes com n complexos (frmulas de Moivre) :

Nota: todas as razes de ndice n tm o mesmo mdulo e os argumentos (no negativos mnimos) esto em progresso aritmtica de razo .

Nota: as n razes de ndice n tm por imagem os vrtices de um polgono regular de n lados, inscrito numa circunferncia de raio .Domnios planos e condies de varivel complexa:

Circunf. de centro z1 e raio r :

Mediatriz do segm. recta entre z1 e z2 :

Semiplano limitado por mediatriz segm rect entre z1 e z2 , ao qual pertence z1 :

Recta vertical x=a+r :

Exemplo:

EMBED Equation.3 representa o semiplano fechado definido pela recta x=a , que fica direita da recta.

Recta horizontal y=b+r :

Semi-recta origem afixo z1 q forma com Ox um ang :

- SUCESSES

Progresso Aritmtica :

Progresso Geomtrica :

- GEOMETRIA

Distncia entre 2 pontos

Mediatriz de [AB] :

Eq. Circunf. centro (x1,y1) raio r : Eq. Elipse Vectores

Soma de vectores Norma vector:

Ponto mdio [AB]

Eq. Vectorial recta

Eq. Paramtricas recta Eq. Cartezianas recta

Declive recta Equao recta q contm P(x1,y1) e declive m: Eq. Reduzida:

Relao entre declives de duas rectas: Produto escalar:

Produto vectorial: ou ng. entre 2 vectores: Projeco: Teorema co-senos

Eq. plano

Eq. geral do plano

reas e Volumes: Curva Normal :

IntervaloProbabilidade EMBED Equation.3 68.27% EMBED Equation.3 95.45% EMBED Equation.3 99.73%

EMBED Equation.3

V ( h , k )

.

x

y

x = h

EMBED Equation.3

ngulo

0 ou 0 rad30 ou EMBED Equation.3 rad45 ou EMBED Equation.3 rad60 ou EMBED Equation.3 rad90 ou EMBED Equation.3 rad

180 ou EMBED Equation.3 rad270 ou EMBED Equation.3 rad

sen

0 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3

1

0

-1

cos

1 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3

0

-1

0

tg

0 EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

--

0

--

Diagrama Argand

x

y

a

c

+a

-a

b

.

.

Elipse

prof_mariocosta@hotmail.com

Tm.: 919 853 327

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