syms x y a;f=exp(-1/(y.^2+x.^2) )sin(x).^2/x.^2(1+1/y.^2).^(x+a.^2*y.^2);L=limit(limit(f,x,1/sqrt(y)),y,inf)
L =
limit(y^(1 - 2a^2y^2 - 2/y^(1/2))sin(1/y^(1/2))^2exp(-y/(y^3 + 1))(y^2 + 1)^(1/y^(1/2) + a^2y^2), y == Inf)