Limiting Recurrence

Calculus Level 3

Let \(f_n(x) \) satisfy the recurrence relation \(f_n (x) =f_1 \big( f_{n-1} (x)\big) \) for \(n=2,3,4, \ldots\) and \(f_1 (x) = \dfrac x2 + 10 \).

Evaluate \( \displaystyle \lim_{n\to\infty} f(x) \).

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