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

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

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

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim\limits_{y \to 0} \frac{{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 }}{{{y^4}}}

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Correct option: A

exists and equals

\frac{1}{{4\sqrt 2 }}

Option A (exists and equals 1/(4√2)) is correct because after rationalizing the numerator twice and simplifying, the limit can be evaluated directly.

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