Consider two differentiable functions \( f(x), g(x) \) satisfying \...

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Consider two differentiable functions \( f(x), g(x) \) satisfying
\( \mathrm{P} \) \( 6 \int f(x) g(x) d x=x^{6}+3 x^{4}+3 x^{2}+c \) and \( 2 \int \frac{g(x) d x}{f(x)}=x^{2}+c \),

W where \( f(x)0 \forall x \in R \).
\[
\lim _{x \rightarrow 0} \frac{\log (f(x))}{g(x)}=
\]
(1) \( e \)
(2) 2
(3) 1
(4) 0
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