Consider the function f(x, y) = (xy2)/(x2 + y4). This is the classic example of a function that has no limit at (0, 0). But the limit as (x, y) approaches (0, 0) along any straight line is always 0.
Maple renders the function by sampling points. This misses the details of what is happening near (0, 0) because the samples are not fine enough here. It looks like the parabolic hill is split in the middle when in fact it is not.
I've modified my ray-tracer to render this function. It shows how the hill joins together at (0, 0).