The fraction is greater than or equal to zero.
By the AM-GM inequality, the denominator is greater than or equal to
2root(2x^2y^4) = 2root(2)xy^2
Therefore, the fraction is less than or equal to
(7x^2y^2) / (2root(2)xy^2) = 7x/2root(2)
Lim x,y->0 (7x/2root(2)) = 0
Hence the...