Quick Qns : Convergence in Polar Coordinates

1. Sep 11, 2009

Legendre

Suppose we investigating the limit of a function on R^2 as (x,y) tend to (0,0).

We convert the function into polar coordinates.

Then "(x,y) tend to (0,0)" is equivalent to "r tend to 0"?

Theta (the angle) does not matter?

2. Sep 11, 2009

Hootenanny

Staff Emeritus
Yes, the angle theta certainly matters. As no doubt you know, a limit it R2 only exists if the value of the limit is independent of the path along which the limit is taken. You would also need to account for theta if, for example, you were asked to compute the limit along a certain path.

3. Sep 11, 2009

HallsofIvy

Staff Emeritus
But if the limit itself exists, the fact that it is independent of the path means that the angle does not matter.

4. Sep 11, 2009

Legendre

Thanks for the input~