Question

find (x^4-y^4)/(x^2+y^2)
as(x,y) goes to(0,0)

Answer 1

x4 -y4=(x2-y2)(x2+y2 than simplify by x2 +y2 and will remain x2-y2

Answer 2

This limit is 0.
You can simplify this equation to \[x^{2}-y^{2}\]
=0-0 = 0

Or
Fix y as a constant. lim x->0 = -y^2. Supose y near zero and you see the answer
Now fix x near zero. lim y->0 = x^2
Both results goes to zero.