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Let \( g(x)=\int_{0}^{x}\left(3 t^{2}+2 t+9\right) d t \) and \( f(x) \) be a decreasing function, \( \forall x \geq 0 \) such that \( A \mathbf{B}=f(x) \hat{\mathbf{i}}+g(x) \hat{\mathbf{j}} \) and
\( \mathrm{P} \) \( A C=g(x) \hat{\mathbf{i}}+f(x) \hat{\mathbf{j}} \) are the two smallest sides of a \( \triangle A B C \)

W \( \lim _{t \rightarrow 0} \lim _{x \rightarrow \infty}\left(\cot \left(\frac{\pi}{4}\left(1-t^{2}\right)\right)\right)^{f(x) g(x)} \) is equal to
(a) 0
(b) 1
(c) \( e \)
(d) does not exist
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