lim _{x rightarrow 0} frac{x^4+x^3+x^2}{sin ^ | vedclass

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(C) We know that for small $x$,$\sin^{-1}\left(\frac{x}{\sqrt{1+x^2}}ight) = 	an^{-1} x$. Substituting this into the limit,we get: $L = \lim_{x i

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$1$

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(C) We know that for small $x$,$\sin^{-1}\left(\frac{x}{\sqrt{1+x^2}}ight) = 	an^{-1} x$. Substituting this into the limit,we get: $L = \lim_{x ightarrow 0} \frac{x^4+x^3+x^2}{(	an^{-1} x)(	an^{-1} x)} = \lim_{x ightarrow 0} \frac{x^2(x^2+x+1)}{(	an^{-1} x)^2}$. Since $\lim_{x ightarrow 0} \frac{	an^{-1} x}{x} = 1$,we can write $(	an^{-1} x)^2 \approx x^2$ as $x ightarrow 0$. $L = \lim_{x ightarrow 0} \frac{x^2(x^2+x+1)}{x^2} = \lim_{x ightarrow 0} (x^2+x+1) = 0^2+0+1 = 1$.

$\lim _{x \rightarrow 0} \frac{x^4+x^3+x^2}{\sin ^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right) \cdot \tan ^{-1} x} = $

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