If the value of \( \lim _{x \rightarrow 0} \frac{\left(1+3 x+2 x^{2...

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If the value of \( \lim _{x \rightarrow 0} \frac{\left(1+3 x+2 x^{2}\right)^{\frac{1}{x}}-\left(1+3 x-2 x^{2}\right)^{\frac{1}{x}}}{x}=k e^{3} \), find the value of \( 12 k \)
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