- #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

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