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Homework Help: One two-variable, and one three-variable limits

  1. Mar 29, 2009 #1
    1. I need to find these two limits, without using the definition of limit:

    a) [tex]
    \mathop {\lim }\limits_{(x,y) \to (0,2)} \frac{{y^2 (x - 2)^2 }}
    {{x^2 (y - 2)^2 }}[/tex]

    b) [tex]
    \mathop {\lim }\limits_{(x,y,z) \to (0,1,1)} \frac{{y + 1}}
    {{\sqrt {z^2 - 1} }}[/tex]
    3. The attempt at a solution

    For a) I found that if looking for the limit using curves, in this case using y-2=mx, with m=constant, and y-2=kx^2, with k=constant, are infinite.

    For b) I'm clueless.

    Any help will be thanked.
  2. jcsd
  3. Mar 30, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    For the second one, note that there is no x-dependency. So you can look at curves in the (y, z)-plane and give them arbitrary x-dependency, i.e. only consider
    [tex]\lim_{(y, z) \to (1, 1)} \frac{y + 2}{\sqrt{z^2 - 1}}[/tex]
  4. Mar 30, 2009 #3
    Yes, I was thinking about that, thanks.
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