Advanced Calculus, Volume 2 |
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apply Exercise Apply Thm assumption bounded c₂ chain rule choose conclusion follows contradiction converge absolutely convergence is uniform Differentiating dist X,S dist Z,T dx exists Exercise 12 Exercise 34 f is continuous f(x+h finite Heine-Borel theorem hence lim holds implies the conclusion implies the result indefinite integral induction integer interval Lemma lim f(x lim s t lim X-X limit point mean value theorem neighborhood nondecreasing obvious one-to-one P₂ PAGES partition proof of Thm real number rectangle containing replace Riemann sum Rolle's theorem S₁ Sect SECTION sequence solution of Exercise subrectangles sufficiently large sum of f Suppose SX f(x triangle inequality uniform convergence uniformly continuous x-xo x-xx Y-Yo yields the conclusion yields the result zero ከወ