Question

Find limit of
f(x,y)=(x^3y^3)/(x^3+y^3) at (x,y)=(0,0)

Answer 1

$lim_{(x,y)\to (0,0)} \frac{x^3y^3}{x^3+y^3}\\ \text{put}y=mx\\ lim_{x\to 0} \frac{x^3}{1+m^3}\\ =0\\ \text{Thus, limit exists and is equal to 0.}$