Homework_Set_4

Homework_Set_4 - can use Mathematica or Maple to do the...

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Math 1a Fall 2005 HOMEWORK SET 4 DUE AT NOON ON MONDAY, OCTOBER 24, 2005 (1) [25 points] Suppose 0 < x n and 0 < y n and that lim n →∞ x n y n = c n = 0 Prove that n =1 x n converges if and only if n =1 y n converges. (2) [25 points] (a) Apostol, page 138, problem 23. (b) Apostol, page 139, problems 28 and 30. You may plot by hand or you
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Unformatted text preview: can use Mathematica or Maple to do the plot. (3) [25 points] Apostol, page 139, problem 31. (4) [25 points] Give an ε, δ proof of the fact that for f ( x ) = 1 / (1 + x ), one has f ′ (0) = − 1. 1...
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This note was uploaded on 03/30/2010 for the course MA 1a taught by Professor Borodin,a during the Fall '08 term at Caltech.

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