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Proving the divergent integral of 1/f(x) as x-> infinity

  1. Jan 18, 2013 #1

    000

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    1. The problem statement, all variables and given/known data
    There exists a function f(x) such that the indefinite integral of 1/f(x) as x-> infinity diverges, and f(x) >= x for all values of x. Prove this function must be a linear polynomial.


    2. Relevant equations
    None that I know of.


    3. The attempt at a solution
    No idea where to start.
     
    Last edited: Jan 18, 2013
  2. jcsd
  3. Jan 18, 2013 #2

    HallsofIvy

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    You can't, as stated, it is not true. There exist many non-polynomial functions that are "asymptotic" to x such that the integral of 1/f(x) diverges. However, if you require that f(x) be a polynomial, then it is true that f must be linear.
     
  4. Jan 18, 2013 #3

    000

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    f(x) must always be larger than x, are there any asymptotic functions that fit that criteria?
     
  5. Jan 18, 2013 #4

    Dick

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    How about f(x)=x+1/x?
     
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