>>12463542intuitively I feel true
it's differentiable, so it's smooth
around 0,0 we have a smooth function with two directions defined. therefore is a linear approximation of the change from 0,0. we know 0,0 is 0 so we have a linear approximation of f as
plugging this in we have a limit with
changing to polar this is
given that this becomes 0 when at 0,0 and that this approaches a perfect approximation of f around 0,0 we can say that expression has a limit of 0 there.
might be missing a part of the argument there somewhere, but i think that's about it
