# Inspired by Jose Sacramento

Calculus Level 5

$\lim_{(a,b)\to \infty}\int_{0}^{a}\int_{0}^{b}\sin\left(\frac{\pi x^2}{2}+\frac{\pi y^2}{2}\right)\, dy\; dx$

Evaluate this limit, rounded to three significant figures.

If you come to the conclusion that this limit fails to exist, enter 666.

Formal Definition: $$\displaystyle \lim_{(a,b)\to\infty}f(a,b)=L$$ means that for every $$\epsilon>0$$ there exists an $$N$$ such that $$|f(a,b)-L|<\epsilon$$ whenever $$a>N$$ and $$b>N$$.

Inspiration

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