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Horizontal asymptote question

  1. Aug 18, 2004 #1
    Well I'm going through an introductory calculus book and right now I'm on the section of horizontal asymptotes.

    Currently I'm stubbed on this:
    y = (x^2 - 1) / (x^2 + 1)

    I take the limit of the function as x increases or decreases without bound and come up with y = 1 being the horizontal asymptote. No problem so far.

    However, the book sketches it so that the curve is always above the asymptote for both + and - infinite.

    The only problem is that if you substitute values for both sides, won't it ALWAYS be under the asymptote (since its a fraction less than one)? There will always be a value of 2 more on the denominator than the numerator.

    So, am I right and the book wrong or what is what ;)
     
    Last edited: Aug 18, 2004
  2. jcsd
  3. Aug 18, 2004 #2
    Yeah, seems like the book is wrong.
     
  4. Aug 18, 2004 #3
    singleton,

    i am also convinced your book is wrong


    regards
    marlon
     
  5. Aug 18, 2004 #4
    The book is wrong. What a strange book. Can you tell us what book it is?
     
  6. Aug 18, 2004 #5
    Calculus (MCA-OAF) by the education ministry of Ontario ;)
     
  7. Aug 19, 2004 #6

    HallsofIvy

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    Science Advisor

    A math book written by an education ministry? That explains it!

    (Probably, the picture got flipped at the printers.)
     
  8. Aug 19, 2004 #7
    It isn't just the picture ;) It describes it the same way heh.
     
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