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Homework Help: Example of funcion that satisfies

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Find example of function that saatisfies ##\lim\limits_{(x,y)\to(0,0)}f(x,y)=0## and ##0\neq\lim\limits_{x\to y}\lim\limits_{y\to0}f(x,y)\neq\lim\limits_{y\to0}\lim\limits_{x\to0}f(x,y)##

    3. The attempt at a solution

    In my opinion it is impossible. Let ##(x_n,y_n)=\left(\frac1n,0\right)## - if ##\lim\limits_{n\to\infty}f(x_n,y_n)## result will not be 0, from Heine definition of limit, the limit will not exist. Please tell me if I am wrong.
     
  2. jcsd
  3. Nov 23, 2013 #2

    LCKurtz

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    Gold Member

    You are correct, assuming you have stated the problem completely and correctly.
     
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