Let $f\left(x\right)=\underset{n\to \infty }{\lim }\frac{x^{2n-1}+a{x}^3+b{x}^2}{x^{2n}+1}$ is continuous for all $x\in R.$ If points $A(-a,3)andB(b+1,-1)$ are points of relative maximum and minimum of a cubic polynomial $y=g\left(x\right),$ then the value of $g\left(2\right)$ is