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If [x] denotes the greatest integer less than or equal to x, then evaluate `lim_(ntooo) (1)/(n^(3))([1^(1)x]+[2^(2)x]+[3^(2)x]+...+[n^(2)x]).`

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To evaluate the limit \[ \lim_{n \to \infty} \frac{1}{n^3} \left( [1^2 x] + [2^2 x] + [3^2 x] + \ldots + [n^2 x] \right), \] we will follow these steps: ...
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