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Math Help - So how do i do these limits?

  1. #1
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    Question So how do i do these limits?

    1) Determine:


    lim
    (x,y)-->(-1,1)__________(x^2 - y^2)/(xy + y^2 + x + y)


    2) Show that it doesnt exist.


    lim
    (x,y)--> (0,0)____________(2xy)/(x^2 + 2y^2)






    If you plug in the numbers for (1) you get 0/0 same with (2), which doesnt seem right at all. Im pretty sure there is suppose to be atleast a few lines of working.
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  2. #2
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    Re: So how do i do these limits?

    Quote Originally Posted by Brennox View Post
    1) Determine:
    lim
    (x,y)-->(-1,1)__________(x^2 - y^2)/(xy + y^2 + x + y)


    2) Show that it doesnt exist.
    lim
    (x,y)--> (0,0)____________(2xy)/(x^2 + 2y^2).
    For the first one note that x^2-y^2=(x+y)(x-y) and xy+y^2+x+y=(x+y)(y+1).
    There is a common factor.
    Last edited by Plato; May 12th 2012 at 08:03 AM.
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  3. #3
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    Re: So how do i do these limits?

    for number (2), if we approach (0,0) along the line x = y, we get a limit of 2/3. if we approach (0,0) along the x-axis, we get a limit of 0. thus the limit cannot exist (any disk centered at (0,0) contains pieces of both lines).
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