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Homework Help: Limit of a squareroot combination.

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data
    find lim x---> infinity
    sqrt(x + sqrt(x)) - sqrt(x)

    2. Relevant equations
    Conjugate multiplication.

    3. The attempt at a solution
    Ok so i know this is probably very easy yet it confuses me.
    Im guessing youd need to multiply the numerator & denominator by the conjugate of the expression, and then work the expression into a form where all the x terms are denominators of a fraction so that as they approach inf, the fraction approaches 0.

    (sqrt(x + sqrt(x)) - sqrt(x))(sqrt(x + sqrt(x)) + sqrt(x))
    / sqrt(x + sqrt(x)) + sqrt(x)

    (x + sqrt(x) +sqrt(x)sqrt(x + sqrt(x)) -sqrt(x)sqrt(x + sqrt(x)) - x)
    / (sqrt(x + sqrt(x)) + sqrt(x))

    / (sqrt(x + sqrt(x)) + sqrt(x))

    this is as far as i get, any help would be appreciated.

    P.s: does this forum have a way of writing maths in a bit more easily comprehendable form?
  2. jcsd
  3. Oct 9, 2009 #2


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    Science Advisor
    Homework Helper

    There should be a guide to using latex somewhere around here.

    [tex]\sqrt{x+\sqrt{x}}=\sqrt{x} \sqrt{1+\sqrt{x}/x}[/tex]

    If you click on that it should pop up a window showing what I typed in. Sorry, I'm not all that good at it. By the way, that's your next step as well.
    Last edited: Oct 9, 2009
  4. Oct 9, 2009 #3
    All right so we have:
    / (sqrt(x + sqrt(x)) + sqrt(x))

    / (sqrt(x) sqrt(1+sqrt(x)/x) + sqrt(x)

    1 / sqrt(1+sqrt(x)/x) + 1

    sqrt(x)/x tends to zero when x ---> infinity

    1 / sqrt(1) +1


    K that makes sense now, thank you.
    And sry bout the lack of latex notation, il look into it for next time!
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