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P9 IMC 2017

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Definisikan barisan fungsi continuously differentiable $f_1,f_2,... :[0.1)\to \mathbb{R}$ dengan rekursi berikut: $f_1=1; f'_{n+1}=f_nf_{n+1}$ di $(0,1)$ dan $f_{n+1}(0)=1$. buktikan kalau $lim_{n\to\infty} f_n(x)$ eksis untuk setiap $x\in [0,1)$ dan tentukan limit tersebut.

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