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  4. If f(x)=| textCos x 1 0 0 2 cos x 3 0 1 2 cos x| then displaystyle lim x arrow π f(x)=

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Q. If $f(x)=\begin{vmatrix}\text{Cos} x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{vmatrix}$ then $\displaystyle \lim _{x \rightarrow \pi} f(x)=$

KCETKCET 2021Determinants

Solution:

$f(x)=4 \cos ^{3} x-3 \cos x$ $=\cos 3 x$
$\displaystyle\lim _{x \rightarrow \pi} \cos 3 x=\cos 3 \pi$
$=-1$