Find Two Paths of Approach from Which One Can Conclude

Multiple Choice

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0) .
- $\text { Define } f ( 0,0 ) \text { in a way that extends } f ( x , y ) = \frac { x ^ { 2 } y ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } \text { to be continuous at the origin. }$

A) f(0, 0) = 1
B) No definition makes f(x, y) continuous at the origin.
C) f(0, 0) = 0
D) f(0, 0) = 2