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Relatively easy limit help please

  1. Aug 2, 2005 #1
    ok... so i'm taking calc3, and didnt go to class for a month, lol

    now i can't solve this (what seems like) a simple limit... please help


    lim
    (x,y,z) -> (0,0,0)

    of this

    xy + yz + zx
    -----------------
    (x^2)+(y^2)+(z^2)




    i tried doing the limit as (x,y,z) approaches (x,0,0) (0,y,0) and (0,0,z) and got zero, but that's not the answer

    however when i put it into my calc and grind it out i get 1... but how can i do it on paper?

    thankyou very much in advance
     
    Last edited: Aug 2, 2005
  2. jcsd
  3. Aug 2, 2005 #2
    The limit does not exist

    To show that, take two curves, e.g:

    [tex]x=y=z[/tex] and [tex]x=y=-z[/tex]

    You'll find [tex]\frac {3x^2} {3x^2}[/tex] and [tex]\frac {-x^2} {3x^2}[/tex]

    Whose limits are 1 and [tex]-\frac {1} {3}[/tex], which are different. CVD
     
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