Show that f(x)=\cos x is uniformly continuous on R.... | Filo
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Answered: (Continuous Extension Theorem). (a) Show that a uniformly continuous function preserves Cauchy sequences; that is, if f : A → R is uniformly continuous and (xn)… | bartleby
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27.2 Show that if f is continuous on ℝ, then there exists a sequence (pn) of polynomials such that pn → f uniformly on each bounded subset of ℝ. Hint: Arrange for |f(x) - pn(x)| < (1)/(n) for |x| ≤ n.
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