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Math Help - Proof by first principles

  1. #1
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    Proof by first principles

    I think i got this right, not sure. Please check for me.

    Let f: R--->R be given by

    f(x)=4x^3 - 3x^2 +1

    Prove from first principles, that f(x)= O(x^3)


    f(x)=4x^3 - 3x^2 +1

    <=4x^3 -3x^3 + x^3=2x^3

    So, does me saying f(x)<=2g(x^3) provide proof? or is there something else i have to do?
    Last edited by Roclemir; August 9th 2009 at 03:41 AM. Reason: type
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  2. #2
    Super Member Gamma's Avatar
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    Dec 2008
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    Not quite right, check your other thread where you asked this. I answered there.

    Your inequalities are not true here actually.

    It is not true that 4x^3 - 3x^2 \leq 4x^3 -3x^3 even for like 2 it fails, so you gotta be a little careful there. You need to make the sign positive, just check the other post.
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