Example of funcion that satisfies

[Chromosom]

Homework Statement

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

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.

 

[LCKurtz]

Homework Statement

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

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.

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