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3-space absolutely convergent apply approximation assume bounded set choose closed curve compute continuous function converges uniformly coordinate Corollary corresponding critical point defined definition described differential equation differential forms direction divergence theorem divergent domain double integral dudv dxdy dxdydz dydz dzdx equivalent evaluate example Exercise exists finite number formula function F given graph Green's theorem grid illustration improper integral integrand interval inverse iterated integral Jacobian Lemma Let f lim F(x limit line segment linear transformation mapping matrix maximum mean value theorem multiple neighborhood notion obtain one-to-one open set orientation origin plane point p0 polynomial proof prove real numbers rectangle region sequence set function set of points Show simple smooth curve solution surface tangent tion unbounded uniformly continuous uniformly convergent variables vector write zero