Limits multivariable calculus

[GDF]

Hello mates
Could someone tell me if a did some mistake in this question? I need to show if the limit exists or not. I found this answer but I'm not sure if I got it right.
Thanks in advance

 

[Steven G]

Of course it is wrong. If (x,y) --> (1,0) then x is approaching 1 and y is approaching 0. But you let x=0, so (x,y) is NOT approaching (1,0).

Also how can x-->(1,0). Maybe if y=0, then (x,y)-->(1,0) but NOT x-->(1,0)