lim _{x rightarrow 0} x^3 left{ sqrt{x^2 + sq | vedclass

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Question

(A) Let $L = \lim _{x \rightarrow 0} x^3 \left( \sqrt{x^2 + \sqrt{x^4 + 1}} - \sqrt{2} x \right)$. As $x \rightarrow 0$,the expression inside the limi

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(A) Let $L = \lim _{x ightarrow 0} x^3 \left( \sqrt{x^2 + \sqrt{x^4 + 1}} - \sqrt{2} x ight)$. As $x ightarrow 0$,the expression inside the limit becomes $0 	imes (\sqrt{0 + \sqrt{0 + 1}} - 0) = 0 	imes (1 - 0) = 0$. Since the expression is $0 	imes 1$,the limit evaluates directly to $0$. Thus,$\lim _{x ightarrow 0} x^3 \left( \sqrt{x^2 + \sqrt{x^4 + 1}} - \sqrt{2} x ight) = 0 	imes (1 - 0) = 0$.

$\lim _{x \rightarrow 0} x^3 \left\{ \sqrt{x^2 + \sqrt{x^4 + 1}} - \sqrt{2} x \right\} = $

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