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\text { Let } b_{n} \text { be a sequence of real numbers satisfying } \sum_{n=1}^{\infty} n 3^{n} b_{n}<\infty \text { Define the function } f(x)=\sum_{n=0}^{\infty} b_{n} x^{n} \text { which is known to have interval of convergence }[-3,3] \text { and to satisfy } \lim _{x \rightarrow 3^{-}} \frac{f(x)}{x-3}=2

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