Differential calculas

  • Thread starter jem05
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
336
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Let f(x,y) = 0 at the origin,
= (cos t , sin t) otherwise ( where x = Rcost ,y =Rsint).
 
  • #3
56
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isnt that the same as f(r,t) = cost , with 0 if r = 0?
 

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