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formulasheet - Some Useful Formulas f x = lim h → f x h f...

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Unformatted text preview: Some Useful Formulas f ( x ) = lim h → f ( x + h )- f ( x ) h (1) Z b a f ( x ) dx = lim n →∞ n X i =1 f ( x i )Δ x Δ x = b- a n (2) Z b a f ( x ) dx ≈ b- a n 1 2 f ( x ) + f ( x 1 )+ ··· + f ( x n- 1 ) + 1 2 f ( x n ) (3) Z udv = uv- Z v du (4) V = Z b a π [ f ( x )] 2 dx (5) Average Value = 1 b- a Z b a f ( x ) dx (6) Total Money Flow = Z t f ( x ) dx (7) P = Z t f ( x ) e- rx dx (8) A = e rt Z t f ( x ) e- rx dx (9) D = f xx ( a,b ) · f yy ( a,b )- [ f xy ( a,b )] 2 (10) F ( x,y,λ ) = f ( x,y )- λ · g ( x,y ) F ( x,y,z,λ ) = f ( x,y,z )- λ · g ( x,y,z ) (11) y i +1 = y i + g ( x i ,y i ) h g ( x,y ) = dy dx , h = x i +1- x i (12) μ = E ( x ) = Z b a xf ( x ) dx (13) Var( x ) = Z b a ( x- μ ) 2 f ( x ) dx = Z b a x 2 f ( x ) dx- μ 2 (14) σ = p Var( x ) (15) f ( x ) = 1 b- a , x ∈ [ a,b ] (16) f ( x ) = ae- ax , x ∈ [0 , ∞ ) (17) f ( x ) = 1 σ √ 2 π e- ( x- μ ) 2 / (2 σ 2 ) , x ∈ (-∞ , ∞ ) (18) z = x- μ σ (19) S n = a ( r n- 1) r- 1 , r 6 = 1...
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formulasheet - Some Useful Formulas f x = lim h → f x h f...

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