Ceil The Limit!

Calculus Level 4

limnx+2x+3x++nxn2 \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,xa,b,x be constants such that the limit above can be expressed as ax+bax + b.

Find the value of a2+b2a^2+b^2.

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