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Is a general sequence possible for the given data?

  1. Oct 20, 2011 #1
    I finished exploring a family of functions

    fk(x) = {xksin(1/x) for x≠0
    {0 for x=0
    for an assignment in my Analysis course, and I'm supposed to determine the highest order derivative that exists and whether or not it's continuous.

    I've noticed a pattern:
    k = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}
    n = {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...},
    where k is a positive integer, and n is the highest order derivative that exists.

    I want to save some space on my page by generalizing these results as a sequence. Is this possible, and if so what's the sequence? Thanks.
     
  2. jcsd
  3. Oct 20, 2011 #2

    Char. Limit

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    Gold Member

    Would n=floor((k-1)/2) work?
     
  4. Oct 21, 2011 #3
    Yes, I figured it out very recently. Thank you.
     
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