$\mathop {\lim }\limits_{y \to 0} {{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 } \over {{y^4}}}$

Question

exists and equals ${1 \over {2\sqrt 2 }}$

exists and equals ${1 \over {4\sqrt 2 }}$

exists and equals ${1 \over {2\sqrt 2 (1 + \sqrt {2)} }}$

does not exists

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