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lim_(y→0) (√(1+√(1+y⁴))-√(2))/y⁴

1. exists and equals 1/(2√(2))
2. exists and equals 1/(4√(2))
3. exists and equals 1/(2√(2)(√(2)+1))
4. does not exist

Correct answer: exists and equals 1/(4√(2))

Solution

The limit can be evaluated using L'Hôpital's rule, which is applicable here since both the numerator and denominator approach zero as y approaches zero. After applying the rule and simplifying, the limit converges to 1/(4√2), confirming that the correct option is B.

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