The value of \( \lim _{x \rightarrow \infty}\left\{\lim _{n \rightarrow \infty} \frac{\left[1^{2...

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The value of \( \lim _{x \rightarrow \infty}\left\{\lim _{n \rightarrow \infty} \frac{\left[1^{2}(\sin x)^{x}\right]+ \left[2^{2}(\sin x)^{x}\right]+\ldots+\left[n^{2}(\sin x)^{x}\right]}{n^{3}}\right\} \) (where [-] denotes the greatest integer function) and math xmlns=http://www.w3.org/1998/Math/MathMLmix/mimo≠/momfencedmrowmn2/mnmin/mimo+/momn1/mn/mrow/mfencedmfracmi mathvariant=normalπ/mimn2/mn/mfracmo /momo,/momin/mimo /momii/mimis/mimo /momii/mimin/mimit/mimie/mimig/mimie/mimir/mi/math is
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