2simple4limple

Calculus Level 5

An Archimedean spiral starting at the origin turns counterclockwise and has its first intersection with $$y = 0$$ at $$x = -\pi$$. The spiral satisfies

$x^{2}+y^{2} = f \left(\frac{x}{y} \right).$

Find $$\displaystyle \lim_{z \rightarrow 0} f(z)$$.

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