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Horizontal Asymptote

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the horizontal asymptote to the graph: f(x) = 2x2/(x4-81)1/2


    2. Relevant equations



    How do I factor the bottom? Because for, the HA, I compare the coefficients.
     
  2. jcsd
  3. Sep 16, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    x4-81=x4(1-81/x4)

    and remember that √(ab)=√a * √b
     
  4. Sep 17, 2009 #3
    How do I prove that the HA: is y=2?
     
  5. Sep 17, 2009 #4

    Mark44

    Staff: Mentor

    Look at
    [tex]f(x)~=~\frac{2x^2}{\sqrt{x^4(1 - 81/x^4)}}[/tex]
    and simplify the denominator.

    What is the limit of f(x) as x gets large in either direction?
     
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