Question

When finding the limit of a function of two variables, is it always better to change it to polar coordinates and find it?

Answer 1

No, sometimes changing to polar coordinates lead to false results

Answer 2

It can lead to a less then desirable method of solving a problem. Some Problems are best solved with xy coordinate while something like a circular in nature problem can best be solved in Polar.

Answer 3

Do lots of practice. The polar method is powerful but only when you fully understand it.