Question

Describe the continuity of the following func:
f(x,y)= [(x^3)+(y^3)]/ [(x^2)+(y^2)]

Answer 1

Infinite discontinuity at f(0,0)

Answer 2

I lied, jump discontinuity at f(0,0)

Answer 3

what if the question is f(x,y)= x/ [(x^2)+(y^2)]

it remains the same, right?

Answer 4

it changes to an infinite discontinuity

Answer 5

yes but it is infinite dis.

Answer 6

daniel are sure the first one is a jump?

Answer 7

Yes, because of L'Hopitals in comes to be 0

Answer 8

f(x,y)=[(x+y)(x^2+xy+y^2)]/[x^2+y^2] nothing cancels so there is no jump unless i'm totally just not thinking

Answer 9

oops f(x,y)=[(x+y)(x^2-xy+y^2)]/{x^2+y^2}

Answer 10

It doesn't matter. Use L'Hopitals with partial derivatives because it comes out to 0/0 if
f(0,0)