If f1x-x2-10- x- R and fnx-f1fn-1x- n- 2-n - N- then evaluate lim n- f n x

f_1(x)=x2+10 f_1^1(x)=12 f_n(x)=f_1(f_n 1(x)) f^1_n(x)=f_1^1(f_n 1(x))f^1_n 1(x)=f^1_n 1(x)2 f^1_n(x)f^1_n 1(x)=12 f^1_n(x)f^1_n 1(x)f^1_n 1 ...

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Algebra of Limits

If f1x=x2+1...

Question

If $f_{1} (x) = \frac{x}{2} + 10 \forall x \in R$ and $f_{n} (x) = f_{1} (f_{n - 1} (x)) \forall n \geq 2, n \in N$ , then evaluate ${lim}_{n \to \infty} f_{n} (x)$

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f_{1} (x) = \frac{x}{2} + 10, \forall x ϵ R

f_{n} (x) = f_{1} (f_{n - 1} (x)), \forall n \geq 2

lim n \to \infty f_{n} (x) = g (x)

\int_{\frac{1}{2} g (x)}^{g (x) - 1} (\frac{s i n x}{1 + x^{a}}) < \frac{2}{g (x) - 2}

f_{1} (x) = \frac{x}{x - 1}

f_{n} (x) = f_{1} (f_{n - 1} (x))

n \geq 2

x

f_{101} (x) = 3 x

f_{1} (x) = \frac{x}{x - 1}

f_{n} (x) = f_{1} (f_{n - 1} (x))

n \geq 2

x

f_{101} (x) = 3 x

f_{1} (x) = | | x | - 2 |

f_{n}) x) = ∣ ∣ f_{n - 1} (x) - 2 ∣ ∣

n \geq 2, n \in N

f_{2015} (x) = 2

f (x) = \frac{3}{4} x + 1,

f^{n} (x)

f^{2} (x) = f (f (x))

n \geq 2, f^{n + 1} (x) = f (f^{n} (x)) .

λ = lim n \to \infty f^{n} (x),

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