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absolutely convergent arbitrary assertion axioms belongs bounded calculation called commutative laws compact interval consider constant continuous function continuously differentiable convex curve defined denote derivative determined divisor elements equal equation example exists exponential function extrema finite follows formula function f(x given Iff(x improper improper integral improper limit induction inequality infinite series integral inverse inverse function Jordan-measurable linear logarithm mapping mathematics matrix mean-value theorem multiplication natural numbers notation obtain oriented parameter parametric representation partition point of accumulation point x0 polynomial power series properties prove quotient radius of convergence rational function rational numbers reader real numbers relative extremum Section sequence shows simplex sub-interval subset sufficiently suppose supremum symbols tangent Taylor series tends termwise differentiation Theorem 16 Theorem 24 trivial true uniformly convergent uniquely variables vector write xu x2 zero