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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: ( ) ( ) dx xdF xf XX = [ ] ( ) = = =≤≤≤≤ d cy b ax XY yxfdYcbXaP ,, [ ] ( ) == =≤≤≤≤ b ax XY d cy dxdyyxfdYcbXaP ,, [ ] ( ) ( )= j i jiXYji yxfyxgYXgE ,.,),( ( )[ ]22 xX mXE −=σ ( ) [ ]jwXeEw =ψ Poisson: α α −⋅= e ! )( x xf x X ασ == 2][ XXE Padronização: X XmXZ σ −= ( ) [ ]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 wd jXE ψ ( ) ( )( ) ( )ygx X Y xg xf yf 1 ' −= = Binomial: xnxX qp x n xf −⋅⋅ =)( npXE =][ npqX = 2σ Exponencial: 0 ,0 ,e)( >>⋅= − λλ λ xxf xX λ σ 1][ == XXE Gaussiana Padronizada: ( ) [ ]zZPzQ >= Uniforme: ab xfX − = 1)( 2 ][ ba XE += ( ) 12 2 2 ab X −=σ TABELA DA GAUSSIANA PADRONIZADA:
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