Let f:(1,∞)→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. Putnamfunctionlimitintegrationalgebradomaingeometry