AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} x^3\left\{\sqrt{x^2+\sqrt{x^4+1}}-\sqrt{2} x\right\}=\)
- A \(0\)
- B \(\frac{1}{2 \sqrt{2}}\)
- C \(\frac{1}{4 \sqrt{2}}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow 0} x^3\left(\sqrt{x^2+\sqrt{x^4+1}}-\sqrt{2} x\right) \\ &= \lim _{x \rightarrow 0} \frac{\left(\sqrt{x^2+\sqrt{x^4+1}}+\sqrt{2} x\right.}{\left(\sqrt{x^2+\sqrt{x^4+1}}+\sqrt{2} x\right.} \\ & \quad \times…
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