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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


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    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
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