1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook