1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Mark44

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limits question and finding oblique asymptote
Loading...