Let \( f:\left( 0,\infty \right) \rightarrow R \) be a differentiable function such that \( f'\left( x \right) =2-\frac { f\left( x \right) }{ x } \) for all \( x\in \left( 0,\infty \right) \) and \( f\left( 1 \right) \neq 1 \). Then:
1
\( \lim _{ x\rightarrow 0+ }{ f'\left( \frac { 1 }{ x } \right) } =1 \)
2
\( \lim _{ x\rightarrow 0+ }{ xf\left( \frac { 1 }{ x } \right) } =2 \)
3
\( \lim _{ x\rightarrow 0+ }{ { x }^{ 2 }f'\left( x \right) } =0 \)
4
\( \left| f\left( x \right) \right| \le 2 \) for all \( x\in \left( 0,2 \right) \)
5
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