1.
For some λ,μ\lambda, \mu, let
f(x)=a+sinxabaa+1+sinxbab1+b+sinxf(x) = \begin{vmatrix} a + \sin x & a & b \\ a & a + 1 + \sin x & b \\ a & b & 1 + b + \sin x \end{vmatrix}

If limx0f(x)x=λ+μa+νb\displaystyle\lim_{x \to 0} \frac{f(x)}{x} = \lambda + \mu a + \nu b, then (λ+μ+ν)2(\lambda + \mu + \nu)^2 is equal to: