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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