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# Formulas - Math 241 Calculus 3 Final Exam Formula Sheet(a...

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Math 241: Calculus 3 Final Exam Formula Sheet (a, b) . (d, e) = a d + b e (a, b) + (d, e) = (a + d, b + e) x (a, b) = (x a, x b) ||(a, b)|| = (a 2 + b 2 ) .5 A pushalong B = ((A . B) / (B . B)) B Equation for a plane: (normal . (x,y,z)) = normal . (point) Equation for the tangent in 2D = (x’, y’) Equation for the normal in 2D = (y’, - x’) OR Equation for the main norm = d/dt (unit tangent) dx = x’ dt, dy = y’ dt, dz = z’ dt Net Flow along = ∫F . (x’, y’) dt Net Flow across = = ∫F . (y’, - x’) dt divField of (a, b) = d/dx (a) + d/dy (b) rotField of (a, b) = d/dx (b) d/dy (a) Gauss-Green: ∫a dx +b dy= ∫∫(d/dx(b)– d/dy(a))dxdy A xy [u, v] = dx/du dx/dv dy/du dy/dv Polar Coordinates: x = r cosθ, y = r sinθ r = ||(x,y)||, θ = x/y angle A xy *r, θ+ = r
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