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Evaluate the limit as y approaches 0: (√(1+√(1+y⁴))-√(2))/y⁴.

1. The limit exists and is 1/(4√(2))
2. The limit exists and is 1/(2√(2)(√(2)+1))
3. The limit exists and is 1/(2√(2))
4. The limit does not exist

Correct answer: The limit exists and is 1/(4√(2))

Solution

The limit can be evaluated using L'Hôpital's rule, which applies because both the numerator and denominator approach 0 as y approaches 0. After applying the rule and simplifying, the result converges to 1/(4√2), confirming that the limit exists.

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