Formulário M008 Capítulos 1, 2, 3 e 4

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FORMULÁRIO – M008 
PRINCIPAIS DIRETIVAS DE DERIVAÇÃO E INTEGRAÇÃO: 
[ ] 0=K
dx
d
 [ ] )(')( xfKxfK
dx
d ⋅=⋅ 
[ ] )(')()( 1 xfxfmxf
dx
d mm ⋅⋅= − 
[ ] )(')ln()()( xfaaa
dx
d xfxf ⋅⋅= 
( )[ ]
)()ln(
)('
)(log
xfa
xf
xf
dx
d
a ⋅
= 
( )[ ] ( ) )(')(cos)( xfxfxfsen
dx
d ⋅= 
( )[ ] ( ) )(')()(cos xfxfsenxf
dx
d ⋅−= 
( )[ ] ( ) )(')(sec)( 2 xfxfxftg
dx
d ⋅= 
( )[ ] ( ) )(')(seccos)(cot 2 xfxfxfg
dx
d ⋅−= 
[ ] )(')()()(')()( xgxfxgxfxgxf
dx
d ⋅+⋅=⋅ 
 
CKxdxK +=⋅ 
C
m
xf
dxxfxf
m
m +
+
=⋅⋅
+
 1
)(
)(')(
1
 
C
a
a
dxxfa
xf
xf +=⋅⋅ )ln(
)('
)(
)( 
( ) +=⋅ Cxfdxxf
xf
)(ln
)(
)('
 
( ) ( ) +−=⋅⋅ Cxfdxxfxfsen )(cos)(')( 
( ) ( ) +=⋅⋅ Cxfsendxxfxf )()(')(cos 
( ) ( )[ ] +=⋅⋅ Cxfdxxfxftg )(secln)(')( 
( ) ( ) +=⋅⋅ Cxftgdxxfxf )()(')(sec2 
( ) ( ) +−=⋅⋅ Cxfgdxxfxf )(cot)(')(seccos 2 
 +




=⋅
+
C
a
xf
arctg
a
dx
xfa
xf )(1
)(
)('
22
 
  ⋅−⋅=⋅ duvvudvu 
FÓRMULAS DE PROBABILIDADE: 
( ) ( )( )AP
BAP
ABP
∩≡| 
( ) ( ) ( )( )AP
BPBAP
ABP
|
| = 
( )BAPBPAPBAP ∩−+=∪ )()()( 
( ) ( )
dx
xdF
xf XX = ( )
( )
( )
( )ygx
X
Y
xg
xf
yf
1
'
−=
= 
[ ] ( )
= =
=≤≤≤≤
d
cy
b
ax
XY yxfdYcbXaP ,, 
[ ] ( )
==
=≤≤≤≤
b
ax
XY
d
cy
dxdyyxfdYcbXaP ,, 
[ ] ( ) ( )=
j i
jiXYji yxfyxgYXgE ,.,),( 
( )[ ]22 xX mXE −=σ 
( ) [ ]jwXeEwj =.ψ 
Padronização: 
X
XmXZ
σ
−= 
Gaussiana Padronizada: ( ) [ ]zZPzQ >= 
( ) [ ]xXPxFX ≤= [ ] ( ) ( )aFbFbXaP XX −=≤< 
[ ] ( )
=
=≤≤
b
ax
X xfbXaP [ ] ( )=≤≤
b
a
X dxxfbXaP . 
( ) ( )
=
=
n
i
iXi
xfxgXgE
1
.)]([ ( )[ ] ( ) ( )
∞
∞−
= dxxfxgXgE X .. 
[ ] ( ) ( )
∞
∞−
∞
∞−
= dxdyyxfyxgYXgE XY ,.,),( 
{ }22222 ][][ XEXEmX xX −=−=σ 2XX σσ = 
[ ] ( ) ( )
0
.
=
−=
w
n
n
nn
dw
jwd
jXE
ψ
 
Binomial: xnxX qp
x
n
xf
−⋅⋅





=)( npXE =][ npqX =
2σ 
Exponencial: 0 ,0 ,e)( >>⋅= − λλ λ xxf xX λ
σ 1][ == XXE 
Uniforme:
ab
xfX −
= 1)( 
2
][
ba
XE
+= ( )
12
2
2 ab
X
−=σ 
Poisson: α
α −⋅= e
!
)(
x
xf
x
X ασ ==
2][ XXE 
 
 
TABELA DA GAUSSIANA PADRONIZADA: