ENAS Final Formula

# 0 2 d fxx x0 y0fyy x0 y0 fxy x0 y0 4 f

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Unformatted text preview: − x0 ) + Fy (x0 , y0, z0 )(y − y0 ) + Fz (x0 , y0, z0 )(z − z0 ) = 0 2 D = fxx (x0 , y0)fyy (x0 , y0 ) − fxy (x0 , y0 ) 4 ∇f (x0 , y0) = λ∇g (x0, y0) g2 (x) b f (x, y )dA = R a h 2 (y ) d f (x, y )dA = R f (x, y ) dy dx g1 (x) f (x, y ) dx dy h 1 (y ) c 1 f (x, y ) dA A R where A is the area of the rectangular region R faverage = β f (r, θ )dA = R ∂r ∂u ∂r ∂u R R ∂r ∂v ∂r ∂v × × ∂r ∂r × ∂u ∂v S= ∂z ∂x f (r, θ ) r dr dθ r 1 (θ ) α n= r 2 (θ ) 2 2 ∂z + ∂y b d dA + 1 dA l f (x, y, z )dV = f (x, y, z )dz dy dx G a c k g2 (x,y ) f (x, y, z )dV = G R f (x, y, z ) dz dA g1 (x,y ) xδ (x, y )dA R δ (x, y )dA x= ¯ R y= ¯ R yδ (x, y )dA R δ (x, y )dA 5 xδ (x, y, z )dV G δ (x, y, z )dV x= ¯ G y= ¯ G z ¯= G yδ (x, y, z )dV G δ (x, y, z )dV zδ (x, y, z )dV G δ (x, y, z )dV θ2 f (r, θ, z )dV = G r 2 (θ ) r 1 (θ ) θ1 g2 (r,θ ) f (r, θ, z ) r dz dr dθ g1 (r,θ ) x = r cos θ, y = r sin θ, z = z f (ρ, θ, φ)...
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