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Old 2006-05-30, 12:53   #3
Damian's Avatar
May 2005

18610 Posts

Thanks for the help. I don't have Rudin's book but neitherway I found the proof here

Now I have another question related to the same theorem.
Suppose the function:

f(x,y) ={ 1 (if x=0 or y=0)
{ 0 (otherwise)

the partial derivatives at the origin are
df/dx = 0 and df/dy = 0

so they exist and are continious.
However the function is not continious in (0,0), so it can't be differentiable there. (there can't be a tangent plane)

What did I misundertood? Because I think the theorem says that if the partial derivatives exists and they are continious then the function is differentiable there.
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