Question

Can someone explain me if this funtion is continuous in point (0,0) and (0,1)
f(x,y)= x^2*sin(y/x) xy is not 0
0 xy=0

Answer 1

For it to be continuous, it must be differentiable at that point. So, find the derivative of that function and see if that derivative has a value at those points.

Answer 2

df/dx (0,0) =0 df/dy(0,0)=0
df/dx (0,1)=0 df/dx(0,0)=cos(inf)

and how should i go on now?
I dont know if derivative has value in this point....every derivative will have a value in some point no?