After re-reading the materials a few times, i think I have a better understanding. May someone check my approach to this question, it is different from the book's approach, however I believe more 'correct' ?

Find the limit, if it exists, or show that the limit does not exist.

I let (x,y) --> (0,0) along any non vertical line through the origin, so y = mx, where m is the slope.

as a result, f(x,y) = f(x,mx) = =

I wasn't quite sure what this end result means, but my taking is that as 'm' varies, or as we pick different slopes, we get different limits, and hence the limit does not exist?

The books method was

approaching (0,0) first from the x-axes and then from the y-axes. As it turns out, the limits were different, but i think my method gives a more generalised answer.

Am I correct in my method, and reasoning about howas 'm' varies, or as we pick different slopes, we get different limits, and hence the limit does not exist?