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Continuous functions with multiple variables

  1. Oct 18, 2005 #1
    I need to find a value for f at (0,0) to make this function continuous:

    f(x,y)=sqrt(x^2+y^2)/[abs(x) + abs(y)^(1/3)]

    With other functions in this problem I simply took the limit .. but taking the limit gives 0/0. In single-variable calculus I would apply l'hopital's rule to this, but I'm not sure what to do with multiple variables.

    I also need to do the same for:

    f(x,y)=(x^2 + y^2)*ln(x^2 + 2y^2)

    For this one, you get 0*0, again an indeterminant form. In single variable I would manipulate it until I got 0/0 and then apply l'hopital .. but I'm lost in multivariable.
  2. jcsd
  3. Oct 18, 2005 #2


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    In f(x,y)=sqrt(x^2+y^2)/[abs(x) + abs(y)^(1/3)] the numerator goes to 0 faster than the denominator (e.g. along x=y); so my guess is f(0,0) = 0.

    0*0 is not indet., it is 0. But ln(0) = -infty so you have -0*infty, which is indet. I don't have an answer for that one (yet).
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