Partial Derivatives in Differential Calculus: Need Help

[jem05]

im trying to get a function R^2 --> R
whose partial derivatives of all orders exist in a neighborhood of (0,0) but it, itself, is not continuous at the origin.
thing is, i think I am thinking of the question wrong because, I am getting examples and checking if partial der. exist but how can i ensure that all the orders do so,...?
any ideas? thx

 

[Eynstone]

Let f(x,y) = 0 at the origin,
= (cos t , sin t) otherwise ( where x = Rcost ,y =Rsint).

 

[jem05]

isnt that the same as f(r,t) = cost , with 0 if r = 0?