Let f ∶ R → R be a function defined as
f(x) = \(\left\{\begin{array}{ll}\frac{\sin (a+1) x+\sin 2 x}{2 x} &, \text {if } x<0 \\b &, \text {if } x = 0 \\\frac{\sqrt{x+b x^{3}}−\sqrt{x}}{b x^{5/2}} &, \text {if } x>0\end{array}\right.\)
If f is continuous at x = 0, then the value of a + b is equal to :
1
\(−\frac{5}{2}\)
2
−3
3
−2
4
\(−\frac{3}{2}\)