Ceil The Limit!

Calculus Level 4

\[ \large \lim_{n\to\infty} \dfrac{ \lceil x \rceil + \lceil 2x \rceil + \lceil 3x \rceil + \cdots + \lceil n x \rceil }{n^2} \]

Let \(a,b,x\) be constants such that the limit above can be expressed as \(ax + b\).

Find the value of \(a^2+b^2\).

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