Limit of function with two variables

Question

lim x²/y²=0

(x,y)→(0,0)

Prove by defination

Answer 1

If we approach via y=x², we can substitute this into your function expression and get the limit of y/y² as y goes to 0. This simplifies to 1/y, and this limit doesn't exist (it blows up to infinity), so your limit as a whole cannot exist either.