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Differential calculas

  1. Mar 25, 2010 #1
    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 im thinking of the question wrong because, im getting examples and checking if partial der. exist but how can i ensure that all the orders do so,...?
    any ideas? thx
     
  2. jcsd
  3. Mar 30, 2010 #2
    Let f(x,y) = 0 at the origin,
    = (cos t , sin t) otherwise ( where x = Rcost ,y =Rsint).
     
  4. Apr 11, 2010 #3
    isnt that the same as f(r,t) = cost , with 0 if r = 0?
     
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