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 relationship proof

  1. Dec 10, 2012 #1
    1. The problem statement, all variables and given/known data
    To establish a big - O relationship, find witnesses C and k such that |f(x)| <= C|g(x)| whenever x > k.

    Show that x^3 is O(x^4) but that x^4 is not O(x^3).

    2. Relevant equations
    If f(x) is O(g(x)) then there is a C such that f(x) <= Cg(x).

    3. The attempt at a solution

    If f(x) is O(g(x)) then there is a C such that f(x) <= Cg(x).
    Thus, if x^3 is O(x^4), then x^3 <= C(x^4).
    This is true for all C > 0 when C is a real number.

    Similarly, if x^4 is O(x^3) then
    x^4 <= Cx^3.
    x <= C (divide both sides by x^3)
    However, x <= C can not be true for any C. Thus x^4 is not O(x^3).

    I'm not sure about this proof because I didn't provide witnesses C and k as the instructions called for. Big-O problems confuse me and I'm not sure if this proof is correct. Any suggestions are appreciated.
  2. jcsd
  3. Dec 11, 2012 #2
    Any suggestions?
  4. Dec 11, 2012 #3
    What is true? x3≤Cx4 if and only if x ≥ 1/C. Perhaps this can help you to find some values of k and C.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook