How do you prove a function of two variables is continuous?

Question

https://i.stack.imgur.com/BdZi1.jpg this question please read and solve

Answer 1

Define delta = 2*epsilon , where epsilon>0...

d=2e

for x,y in (-d,d), F(d,d) = d^3*d/(d^3+d^3)

= d^4/(2d^3)

= (1/2)d

= (1/2)(2e)

= e<=e

so for e>0 there is d=2e such that F(d,d) <=e