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Homework Help: Limit Problem

  1. May 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Lim as x goes to infinity of sqrt(x^2 + 1) / x

    3. The attempt at a solution

    know you are supposed to divide by the highest power of x, but how does that work when you have an x^2 within a sqrt?
  2. jcsd
  3. May 14, 2009 #2


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    Gold Member

    Try writing x2+1 as x2(1+1/x2).

    See if that helps.
  4. May 15, 2009 #3


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    Science Advisor

    And remember that [itex](1/x)\sqrt{x^2+ 1}= \sqrt{(1/x^2)(x^2+ 1}[/itex]
  5. May 16, 2009 #4
    put your x in to the square root by making it X^2....then it will be easy because you will get something like
    limit x--->infinity sqrt(1+1/X^2)
    and when x goes to infinity 1/X^2 goes to zero
    so your final limit will go to 1
    hope you got it!!!!!!!!!!!!
  6. May 16, 2009 #5


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    Science Advisor

    You've got three responses saying the same thing in different ways!
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