Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to find out asymptotes for any algebraic curve?

  1. Jan 13, 2014 #1
    There are a lot of contents regarding finding vertical, horizontal and oblique asymptotes for the so called 'rational' functions online. All of these curves are given in the form y=f(x)=(g(x))/(h(x)).
    But as far as my search results go, there are none regarding general algebraic curves/polynomials.
    I'd like to know, for example, how do you find all the asymptotes for the curve:
    [itex]y^3 - x^2y + 2y^2 +4y + x = 0[/itex]
    i.e. for a curve of the form:
    [itex]f(x,y) = 0[/itex] where an explicit definition for [itex]y[/itex] has not been provided or would be inconvenient?
     
  2. jcsd
  3. Jan 13, 2014 #2

    epenguin

    User Avatar
    Homework Helper
    Gold Member

    Well that one you find them by looking what happens when x and y become very large and you can neglect certain terms as being numerically negligible compared to certain others.
     
    Last edited: Jan 13, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to find out asymptotes for any algebraic curve?
  1. Finding asymptotes (Replies: 2)

Loading...