# Limiting behavior of the area of an infinity-gon

Calculus Level 3

Suppose a regular $$n$$-gon is constructed from $$N$$ sides of constant length $$2\sqrt{\pi}$$.

As the number of sides $$N$$ of this $$n$$-gon is increased towards infinity, which function of $$N$$ gives the limiting behavior of of the $$n$$-gon's area, $$A(N)$$?

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