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Big O analysis

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data

    4. Give a c > 0 and an integer n0 ≥ 1 such that, for all n ≥ n0.

    b. 16n log (n²) ≤ cn²

    The answer (from the sheet) is c = 32

    2. Relevant equations

    3. The attempt at a solution
    When I attempt to solve such an equation I start at n=1, then go to n=2. but that way I get the answer c=17.

    I understand this is kind of a brute force attack. I would like to know what the proper way would be to solve this equation.
    Last edited: Nov 7, 2011
  2. jcsd
  3. Nov 7, 2011 #2
    You can fiddle with the equation a little to get

    32 log(n)/n ≤ c

    Then you can graph it to find the maximum of the left-hand-side. However, that turns out to be about 11.72 for n = 3. (Presuming n is an integer.) Maybe I'm misinterpreting something -- I don't see where the "32" answer comes from, or your "17" for that matter.
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