Limiting Recurrence

Calculus Level 3

Let fn(x)f_n(x) satisfy the recurrence relation fn(x)=f1(fn1(x))f_n (x) =f_1 \big( f_{n-1} (x)\big) for n=2,3,4,n=2,3,4, \ldots and f1(x)=x2+10f_1 (x) = \dfrac x2 + 10 .

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

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