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Let $$f : (0, \infty) \rightarrow R$$ be a differentiable function such that $$f'(x) = 2 - \frac{f(x)}{x}$$ for all $$x \in (0, \infty)$$ and $$f(x) \neq 1$$. Then
$$\lim_{x \rightarrow 0+}f'\left(\frac{1}{x}\right) = 1$$
$$\lim_{x \rightarrow 0+}xf\left(\frac{1}{x}\right) = 2$$
$$\lim_{x \rightarrow 0+}x^2 f'(x) = 0$$
$$\mid f(x) \mid \leq 2$$ for all $$x \in (0, 2)$$
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