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Analysis problem

  1. Dec 7, 2004 #1
    Please help with the following problem:

    Find an example of a finction f:R-R where

    lim x tends towards zero of xf(1/x) is not zero
     
  2. jcsd
  3. Dec 7, 2004 #2

    Galileo

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    It would obviously be the case when f(1/x) can cancel the x, so that the limit is independent of x.
    What would f(x) have to be, if f(1/x) is to be proportional to 1/x?
     
  4. Dec 7, 2004 #3
    Would f(x) have to be -x squared if f(1/x) is to be proportional to 1/x
     
  5. Dec 7, 2004 #4

    dextercioby

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    Hint:Relabel 1/x with "lambda",get the old function f(1/x) in terms of "lambda" and then simply rename "lambda" as being x.U'll get your answer.
     
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