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Find c likes the series is convergent

  1. Apr 11, 2009 #1
    Find c ∈ IR, like ∫∞ ( 2x - c ) dx is convergent
    0 X^2 +1 2x+1

    I need your help because I was trying to resolve the problem, but I couldn't, is difficult for me.
    Please help me!!
     
  2. jcsd
  3. Apr 12, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi marrie! Welcome to PF! :smile:
    hmm :rolleyes: … you mean [tex]\int_0^{\infty}\left(\frac{2x}{x^2+1} - \frac{c}{2x+1}\right)dx[/tex] :wink:

    Hint:

    i] can you integrate each of them separately? does each converge or diverge?

    ii] how much faster do you think the bottom needs to increase than the top for the integral to converge? :smile:
     
  4. Apr 13, 2009 #3
    Ok, if I integrate each of them separately, I believe that the series diverge.
    And I know that the bottom needs to increase than for the top for the integral converge.
    thanks for your hints!!!
     
  5. Apr 14, 2009 #4

    tiny-tim

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    Hi marrie! :smile:
    ah … but how much more than the top? :wink:

    anyway, write the whole thing over a common denominator …

    then what does c have to be to make the top increase slowly enough? :smile:
     
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