they say I can use x=y => it will have 2 limitf(x,y)= (xy)/x^2+y^2
prove there is no value for f is continuous at (0,0).
but I don't know how to do it.
PlX Help...
It helps to finish asking the question ....
You should have been taught how to tale limits along different paths. Along the x-axis, y = 0. Taking the limit x --> 0 your function clearly approaches 0.
Along the line y = x, you need to consider $\displaystyle \displaystyle \lim_{x \to 0} \frac{x^2}{x^2 + x^2}$.
Are these two limits the same? Draw a conclusion.