# Calculus problem #2130

Calculus Level 3

Evaluate $$\displaystyle N = \lim_{x \to \infty} \left(\sqrt{\left \lfloor x^2+x \right \rfloor}-x \right)$$.

Details and assumptions

The function $$\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$$ refers to the greatest integer smaller than or equal to $$x$$. For example $$\lfloor 2.3 \rfloor = 2$$ and $$\lfloor -5 \rfloor = -5$$.

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