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Finding limits of 2 varible functions

  1. Sep 26, 2009 #1
    1. The problem statement, all variables and given/known data


    Find the limit, if exist, otherwise show why it doesn't;

    F(x,y) = R;

    where R =

    x^2 + y^2
    ------------------------
    sqrt( x^2 + y^2 + 1) - 1


    Attempt :

    |R| = R

    Since I know that |x| <= sqrt(x^2) <= sqrt(x^2 + y^2 + 1) = J

    R <= J^2 + J^2 / (J + 1) = 2*J^2 / (J + 1)

    Stuck here.

    Also does the methods of 1 variable function to find limits, such as l'hopital rule apply to 2 variable? I assume not, since the book has not mentioned it.
     
  2. jcsd
  3. Sep 26, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    i assume it is at the limit at the point (0,0) you're trying to investigate?
     
  4. Sep 27, 2009 #3
    Suggestion: Go back to the beginning and rationalize the denominator.
     
  5. Sep 27, 2009 #4
    Perfect. Should have seen that. Thank you.
     
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