Prove That the Following Limit Does Not Exist $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } f ( x , y )$

Essay

Prove that the following limit does not exist: $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } f ( x , y )$ where $f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 4 } }$ .