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Can anybody explain this to me?

  1. Nov 8, 2012 #1
    In this link:


    http://people.ischool.berkeley.edu/~johnsonb/Welcome_files/104/104hw9sum06.pdf [Broken]

    For number 28.8 b),

    ...for case 1, they say that x is the limit for the sequnce <x_n>, right? So doesn't the limit for the sequence <f(x_n)> need to be x^2? Why does the answer say that it must be zero?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 8, 2012 #2

    lurflurf

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    That would be true for f continuous, which the exercise is proving to be false. That approach seems a bit complicated.
    if x_n is always rational
    lim <f(x_n)>=0
    if x_n is never rational
    lim <f(x_n)>=x^2

    they agree if and only if x=0
     
  4. Nov 8, 2012 #3

    tiny-tim

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    Hi Artusartos! :smile:
    No, it says limn->∞xn2 = x2 0. :wink:

    (not equal to)
     
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