Let e = epsilon and d = delta

We need to find a d st if x^2 + y^2 < d^2

then| xy - 0| = |xy| < e

in terms of polar coordinates xy = r^2cos(t)sin(t)

It follows |xy| < r^2 = x^2 + y^2

take d = sqrt(e)

then if x^2 +y^2 < d^2 |xy| < e

It should be fairy obvious is false

since if you approach (0,0) along the line y = x the limit is infinity