Limiting the partition

Calculus Level pending

Given \( f(n+1)=\frac { 1 }{ 2 } \left\{ f(n)+\frac { 9 }{ f(n) } \right\} \) for natural numbers \(n\) for \(f(n)>0\). Evaluate \( \displaystyle\lim_{n\to\infty} f(n) \).

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