1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook