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3-space absolutely convergent An+1 apply b₁ b₂ boundary bounded set choose closed curve compute continuous function coordinate Corollary corresponding defined definition derivative differential forms divergent domain dudv dxdy dxdydz dydz dzdx equivalent evaluate example Exercise exists f is continuous f(po f(xo formula function f ƒ and g given graph Green's theorem improper integral integrand interval inverse Jacobian Let f Let f(x lim f(x line segment linear transformation mapping matrix mean value theorem neighborhood obtain one-to-one open set orientation p₁ plane polynomial proof prove R(Ap real numbers rectangle region sequence set of points Show smooth curve surface T(po uniformly continuous uniformly convergent variables vector write zero ди ду дх მყ