# Area under curve?

Calculus Level pending

$\lim_{n \to \infty} (x^2+y^2)^\frac 1 n =\arctan_{n}(e^{\arctan \left(\frac yx \right)}-1)$

Find the area of loops of the curve above.

Notation: $$\arctan_{n}$$ represent a function $$\arctan (\cdot)$$ repeated $$n$$ times, for example: $$\arctan_3 (x)=$$ $$\arctan(\arctan(\arctan(x)))$$.

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