lim y→0 √1+√1+y^4−√2 / y^4

Question

$\lim\limits_{y\to0} {\sqrt{1+\sqrt{1+y^4}}-\sqrt2\over y^4}$

(1) exists and equals $1\over4\sqrt2$

(2) does not exist

(3) exists and equals $1\over2\sqrt2$

(4) exists and equals $1\over2\sqrt2(\sqrt2+1)$