Defining a function at some given point to make it continuous So I have a function 
$$ f(x,y) = \frac{xy(x^2-y^2)}{x^2+y^2} $$
I have to define the function at $(0,0)$ so that it is continuous at origin. Is there any general approach we follow in this type of problems?  I am not sure but I think Sandwich Theorem has to be applied and some suitable function has to be taken . 

Please check out the new answer
$$ |xy(x^2-y^2)|  <= |xy||(x^2-y^2)| <= |x||y||x^2+y^2|$$
Now,
$$ |x||y||(x^2+y^2)| =  \sqrt(x^2)\sqrt(y^2)|x^2+y^2| <= (\sqrt{(x^2+y^2)})(\sqrt{(x^2+y^2)})|x^2+y^2| $$
The last expression is nothing but $(x^2+y^2)^2$ . Therefore 
$$    \frac{ |xy(x^2-y^2)| }{(x^2+y^2)}<=\frac{(x^2+y^2)^2}{(x^2+y^2)} $$
Thus the Sandwich theorem can be applied now
Then, 
$$-(x^2+y^2) < f(x,y) < (x^2+y^2) $$
And I enforce the limit $(0,0)$ which gives $f(x,y)$ as $0$.
