Give an example of a function f:R^2 --> R where both partial derivatives df/dx and df/dy exist non-trivially, but neither are continuous at (0,0).
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Anonymous2007-08-29 18:09 ID:u8Y/NBHX
I'd assume some function of the form
f(x,y) = xsin1/x + ysin1/y
should suffice.
I'm extrapolating from my knowledge of functions of a single parameter, but xsin1/x and ysin1/y are both continous functions, so I'd assume the addition would be continous.
However df/dx|y isn't continous and neither is df/dy|x.