anonymous
  • anonymous
Describe the continuity of the following func: f(x,y)= [(x^3)+(y^3)]/ [(x^2)+(y^2)]
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Infinite discontinuity at f(0,0)
anonymous
  • anonymous
I lied, jump discontinuity at f(0,0)
anonymous
  • anonymous
what if the question is f(x,y)= x/ [(x^2)+(y^2)] it remains the same, right?

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anonymous
  • anonymous
it changes to an infinite discontinuity
myininaya
  • myininaya
yes but it is infinite dis.
myininaya
  • myininaya
daniel are sure the first one is a jump?
anonymous
  • anonymous
Yes, because of L'Hopitals in comes to be 0
myininaya
  • myininaya
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
myininaya
  • myininaya
oops f(x,y)=[(x+y)(x^2-xy+y^2)]/{x^2+y^2}
anonymous
  • anonymous
It doesn't matter. Use L'Hopitals with partial derivatives because it comes out to 0/0 if f(0,0)

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