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
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.
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?
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