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Homework Help: Limit to infinity question

  1. May 13, 2009 #1
    1. The problem statement, all variables and given/known data

    lim_x->∞ of [√x + 2|x|] / [1 + x]

    2. Relevant equations
    lim_x->∞ of 1/[x^n] = 0


    3. The attempt at a solution
    Hi everyone,

    Here's what I've done so far:

    I divided top and bottom by the highest power of x, i.e. x.
    So:
    [x^-1/2 +/- 2] / [1/x + 1]

    And taking the limit of x to ∞ of this:
    [0 +/- 2] / [0 + 1] = +/- 2

    Is this correct?

    Thanks for any help.
     
  2. jcsd
  3. May 13, 2009 #2

    gabbagabbahey

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    Why is there a [itex]\pm[/itex] in your answer?...Surely you recognize that [itex]x[/itex] is positive as it approaches [itex]+\infty[/itex]?
     
  4. May 13, 2009 #3
    Thanks, I didn't think about that. But is it correct apart from that?
     
  5. May 13, 2009 #4

    gabbagabbahey

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