Clever. I definitely figured it "had" a limit that varies by path - I'm not a mathematician but I instinctively distrust singularities like this one's 0/0. But it's a surprise to see a function whose limit varies between the linear and nonlinear paths.
It feels like you should end with at least pointing out that there isn't actually a limit, in epsilon-delta terms. Or to the concept of limit superior and limit inferior. Or otherwise treat this as an intro to more-serious stuff.
