Is f(x)=1/x discontinuous at point x=0 or not since its domain is x>0 and x<0?
And what about f(x,y)=$\frac{xy^2}{x^2+y^2}$ continuity?
And Df(x,y) exist or parcial derivatives are continuous?because if f(x,y) is not define at (0,0) then partial derivatives are not define for that point hence Df is derivable is that true or not and why?
You're right since the function $$f(x) =\frac{1}{x}$$ is not defined at point $x=0$ it cannot be discontinuous at this point. Analogously the function $$f(x,y)=\frac{xy^2}{x^2 +y^2}$$ is continuous in whole its domain. Moreover the function $$f(x,y) =\begin{cases} \frac{xy^2}{x^2 +y^2} \mbox{ for } (x,y)\neq (0,0) \\ 0 \mbox{ for } (x,y)= (0,0)\end{cases}$$ is also continuous. Similary if a function is not defined at any point then you cannot talk about partial derivatives at this point.