If \( \lim _{x \rightarrow 1}\left(1+a x+b x^{2}\right)^{\frac{c}{x-1}}=e^{3} \), then find cond...

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If \( \lim _{x \rightarrow 1}\left(1+a x+b x^{2}\right)^{\frac{c}{x-1}}=e^{3} \), then find conditions on \( a, b \) and \( c \).
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