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AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2+x^5+x^6}}{x^4}=\)

  1. A \(\frac{1}{4 \sqrt{2}}\)
  2. B \(\frac{1}{2 \sqrt{2}}\)
  3. C \(\frac{1}{\sqrt{2}}\)
  4. D \(\frac{1}{3 \sqrt{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{4 \sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\(\lim _{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2+x^5+x^6}}{x^4}\) \(=\lim _{x \rightarrow 0} \frac{\left(\sqrt{1+x^4}-x^5-x^6-1\right)}{x^4\left(\sqrt{1+\sqrt{1+x^4}}+\sqrt{2+x^5+x^6}\right)}\)…