Using polar co-ordinates to prove a bivariate limit exists at the origin.
In order to prove a limit at exists for a function of form ,
where ,
we must show that the limit is the same from all directions of approach.
In order to make this easier,
we can convert the input from cartesian form to polar form ,
where and .
Since corresponds to ,
it is only necessary to show the limit of the converted function as regardless of .
Often this will involve the Squeeze Theorem.