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If $f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{array}\right|$, then $\lim _{x \rightarrow \pi} f(x)$ is equal to
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If $f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{array}\right|$
Expand along $C_{1}$,
$\begin{aligned}
&=\cos x\left(4 \cos ^{2} x-3\right) \\
&=4 \cos ^{3} x-3 \cos x \\
&=\cos 3 x \\
\therefore \lim _{x \rightarrow \pi} \cos 3 x=\cos 3 \pi=-1
\end{aligned}$
Expand along $C_{1}$,
$\begin{aligned}
&=\cos x\left(4 \cos ^{2} x-3\right) \\
&=4 \cos ^{3} x-3 \cos x \\
&=\cos 3 x \\
\therefore \lim _{x \rightarrow \pi} \cos 3 x=\cos 3 \pi=-1
\end{aligned}$
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