Which of the following is false about
$ \lim_{y \to 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4} $
(A) limit exists and equal to $ \frac{1}{4\sqrt{2}} $
(B) limit does not exist
(C) limit exists and equal to $ \frac{1}{2\sqrt{2}} $
(D) limit exists and equal to $ \frac{1}{2\sqrt{2}(\sqrt{2}+1)} $
(a) A, B, C
(b) B, C, D
(c) A, B, D
(d) A, C, D