If lim x→0 |(a+sinx/x 1 1), (a 1+sinx/x) 1, (a 1 a+sinx/x)|

Question

If \(\lim _{x \rightarrow 0}\left|\begin{array}{ccc}a+\frac{\sin x}{x} & 1 & 1 \\ a & 1+\frac{\sin x}{x} & 1 \\ a & 1 & a+\frac{\sin x}{x}\end{array}\right|\)  

\(=\mu a^2+\lambda a+\alpha, \text{then}\ \mu+\lambda+\alpha\) is

Answer 1

Correct option is "4"  

\(\left|\begin{array}{ccc}a+1 & 1 & 1 \\ a & 2 & 1 \\ a & 1 & a+1\end{array}\right|=a^2+2 a+1\)  

\(\therefore \mu=1\)

\(\lambda=2\)

\(\alpha=1\) 

\(\therefore \quad \mu+\lambda+\alpha=4\)