MathDB
Putnam 2009 B5

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December 7, 2009
Putnamfunctionlimitintegrationalgebradomaingeometry

Problem Statement

Let f:(1,∞)→R f: (1,\infty)\to\mathbb{R} be a differentiable function such that f'(x)\equal{}\frac{x^2\minus{}\left(f(x)\right)^2}{x^2\left(\left(f(x)\right)^2\plus{}1\right)} \text{for all }x>1. Prove that \displaystyle\lim_{x\to\infty}f(x)\equal{}\infty.
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