Let \(f:R\to R\) be a function defined as \(f(x)=\left{\begin{matrix}\frac{\sin (a+1)x+\sin 2x}{2x},\text{ if }x 0\end{m…

Let \(f:R\to R\) be a function defined as

\(f(x)=\left{\begin{matrix}\frac{\sin (a+1)x+\sin 2x}{2x},\text{ if }x<0 \\ b,\text{ if }x=0 \\ \frac{\sqrt{x+b{x}^{3}}-\sqrt{x}}{b{x}^{5/2}},\text{ if }x>0\end{matrix}\right.\)

If \(f\) is continuous at \(x=0\), then the value of \(a+b\) is equal to: