Question

If$f\left(x\right)=\left|\begin{array}{ccc}\cos x& 1& 0\\ 1& 2\cos x& 1\\ 0& 1& 2\cos x\end{array}\right|$ then $\underset{x\to 0}{lim}f\left(x\right)=$

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

Determinant of the given matrix equals to $f\left(x\right)$.

Thus $f\left(x\right)=cosx\left[\right(2cosx\left)\right(2cosx)-1)]-1(2cosx)-0$

$\therefore$ $f\left(x\right)=cosx(4co{s}^{2}x-1)-\left(2cosx\right)$

Now applying the limit $x\to 0$ to $f\left(x\right)$

We get ${lim}_{x\to 0}f\left(x\right)$ $=1\left[4\right(1)-1]-(2\times 1)$ $(\because cos0=1)$
$⟹$ ${lim}_{x\to 0}f\left(x\right)$ $=3-2=1$