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Limit with unknown constants

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    find limit of x as it approaches infinite sqrt(x^2+ax)-sqrt(x^2+bx)
    a and b are not given

    2. Relevant equations



    3. The attempt at a solution
    Looking at this equation I first eliminated the square roots. After simplifying i ended up with ax-bx/sqrt(x^2+ax)+sqrt(x^2+bx) I think that this problem cannot be solved b/c a and b are not given. Is this right or is there another way of solving this?
     
  2. jcsd
  3. Sep 27, 2009 #2
    You can't have ax-bx because that basically turns out to be ∞-∞. So you need to pull out x from the square roots so you can cancel out the x's in the numerator.

    [tex]\frac{ax - bx}{\sqrt{x^2 + ax} + \sqrt{x^2 + bx}} = \frac{ax - bx}{\sqrt{x^2(1 + \frac{ax}{x^2})} + \sqrt{x^2(1 + \frac{bx}{x^2})}} = \frac{ax - bx}{x\sqrt{1 + \frac{a}{x}} + x\sqrt{1 + \frac{b}{x}}}[/tex]

    See where you can go from there.
     
  4. Sep 28, 2009 #3
    thank you
     
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