I am not saying I agree with the answer, just that I have never tried that approach before. One problem with letting x=rcos(t) and y=rsin(t) is that it limits curve to travel at any point on the unit circle (assuming r=1 for arguments sake) for any value of t, which supports your comment about this problem's ability to have a limit that exists. Since we do not know where the problem came from (text book, etc). It could be that limit does not exist as stated and the sources answer is wrong to begin with. My next thought on this problem is to rewrite the numerator using identities and break it up into two separate limits and see where that goes.