Area under curve?

Calculus Level pending

lim ⁡ n → ∞ ( x 2 + y 2 ) 1 n = arctan ⁡ n ( e arctan ⁡ ( y x ) − 1 ) \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 \arctan_{n} represent a function arctan ⁡ ( ⋅ ) \arctan (\cdot) repeated n n times, for example: arctan ⁡ 3 ( x ) = \arctan_3 (x)= arctan ⁡ ( arctan ⁡ ( arctan ⁡ ( x ) ) ) \arctan(\arctan(\arctan(x))) .


The answer is 0.

Subh Mandal by subh mandal , 22, India

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1 solution

Subh Mandal
Sep 7, 2016

Arctan(n) where n is very large number diminishes any quantity to 0 by raising such number to n we further diminish it and get a point circle so area is zero.

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