AP EAMCET · Maths · Limits
\(\lim _{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}=\)
- A \(\frac{1}{4 \sqrt{2}}\)
- B \(\frac{1}{2 \sqrt{2}(1+\sqrt{2})}\)
- C \(\frac{1}{2 \sqrt{2}}\)
- D \(\frac{1}{4 \sqrt{2}(1+\sqrt{2})}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{4 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\( \lim _{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4} = \lim _{y \rightarrow 0} \frac{(\sqrt{1+\sqrt{1+y^4}}-\sqrt{2})(\sqrt{1+\sqrt{1+y^4}}+\sqrt{2})}{y^4(\sqrt{1+\sqrt{1+y^4}}+\sqrt{2})} \)…
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