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Homework Help: Limits question and finding oblique asymptote

  1. Oct 14, 2011 #1
    Question: Guess the oblique asymptote of the graph f(x) for x→∞. Write down the limit you have to compute to prove that your guess is correct.

    f(x)= [itex]\sqrt{(x^{4}+1)/(x^{2}-1)}[/itex]
    so the limit would be: lim x→∞ [itex]\sqrt{(x^{4}+1)/(x^{2}-1)}[/itex]

    I sketched out a graph but I just have no clue how to compute for the oblique asymptote. The professor explained that you have to use the polynomials in long division but I don't fully understand how to yet.
  2. jcsd
  3. Oct 14, 2011 #2


    Staff: Mentor

    An oblique asymptote is a straight line y = ax + b that the graph of the function approaches for large x or very negative x.

    Use polynomial long division to carry out the division of the rational expression inside the radical. You should get x2 + some other terms. Then, factor out x2 from each term inside the radical so that you have x2(1 + <other stuff>). At this point you can simplify the radical somewhat.

    I'm sure there's a topic on wikipedia for polynomial long division. Open wikipedia and do a search using "polynomial long division" if you don't understand this process.
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