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Find horizontal asymptotes of a radical function

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the horizontal asymptotes for the following equation:



    2. Relevant equations
    [tex]
    f(x) = \sqrt{x^2+4x}-\sqrt{x^2+x}
    [/tex]


    3. The attempt at a solution
    First I factored f(x):
    [tex]
    f(x) = \sqrt{x}\sqrt{x+4}-\sqrt{x+1}
    [/tex]
    Then I conjugated it:
    [tex]
    f(x) = \frac{x(x+4-x+1)}{\sqrt{x}\sqrt{x+4}-\sqrt{x+1}}
    [/tex]
    That's as far as I've been able to get. Any help would be appreciated.

    edit: I "cheated" by plugging in big numbers and found the asymptote is y= -1.5
     
    Last edited: Mar 24, 2009
  2. jcsd
  3. Mar 24, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    do you mean (plus sign on denominator & brackets)
    [tex] f(x) = \frac{x[x+4-x+1]}{\sqrt{x}(\sqrt{x+4}+\sqrt{x+1})}[/tex]

    i would start with
    [tex] f(x) = \frac{3x}{\sqrt{x^2+4x}+\sqrt{x^2+x}} [/tex]

    now try taking x outside the denominator and cancelling with numerator (or equivalently multiply both by 1/x)

    then take the limit as x goes to +- infinity
     
    Last edited: Mar 24, 2009
  4. Mar 24, 2009 #3
    I fixed the brackets, and I'll try that tomorrow (I'm going to bed now). Thanks.
     
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