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Multivariable limits with CAS

  1. Mar 15, 2009 #1
    1. The problem statement, all variables and given/known data
    I would like to be able to compute multivariable limits with a CAS. I have Mathematica, Derive and an HP 50g.
    For example, how would I compute:
    [tex]\lim_{(x,y)\rightarrow(0,0)}\frac{x^2}{y}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    On Mathematica I tried:
    Code (Text):
    Limit[x^2/y, {x, y} -> {0, 0}]
    (doesn't work)
    Code (Text):
    Limit[x^2/y /. {y -> f[x]}, x -> 0]
    (I think this could work, but I need to figure out what f[x] has to be)

    Thanks for your help.
     
  2. jcsd
  3. Mar 15, 2009 #2
    The limit in your example does not exist (it is undefined), because it depends on how you approach (0,0). For example, f(t,t)->0 as t->0 from the right, but f(sqrt(t),t)->1 as t->0 from the right.
     
  4. Mar 15, 2009 #3
    OK, sorry for choosing a wrong example, I'm just starting multivariable calculus. Anyway for existing limits, is there any way to compute them using a CAS?
     
  5. Mar 15, 2009 #4

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Here's a nice little example using mathematica. Contour Plots are typically a good way to infer whether a limit exists before you go ahead and calculate it.
     
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