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Finding the limit of x/sqrt(x^2 + 1) as x--> +infty

  1. Mar 26, 2008 #1
    1. The problem statement, all variables and given/known data

    I need to find the limit of (x/sqrt(x^2 + 1)) as x goes to infinite for an infinite sequences problem.

    2. Relevant equations

    3. The attempt at a solution
    I thought I would do L'H rule but I continually get infinite/infinite type does this mean it does not exist?
  2. jcsd
  3. Mar 26, 2008 #2


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    Gold Member

    Try simplifying the expression by dividing both the numerator and denominator by x (so overall you've just multiplied by x/x=1 and haven't changed the expression). You'll be left with something you can find the limit of without having to use L'Hopital's rule.
  4. Mar 26, 2008 #3
    So I did that and I got 1 / [(x+1)/(x^2)]^(1/2)
    Last edited: Mar 26, 2008
  5. Mar 26, 2008 #4
    Right, now simplify everything in the square root sign and you'll find that the equation reduces to something you can easily take the limit of as x-> infinity

    Edit: By simplify I mean expand the fraction as two fractions over [itex] x^2 [/itex]. Also I believe that you mean [itex] \sqrt{\frac{x^2+1}{x^2}} [/itex]
    Last edited: Mar 26, 2008
  6. Mar 26, 2008 #5
    yes I get it now I messed up with one of the x's in the denominator not being squared thanks everyone
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