Let \( f: R \rightarrow R \) be a function defined as \[ f(x)=\left\{\begin{array}{cc} \frac{\si...

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Let \( f: R \rightarrow R \) be a function defined as
\[
f(x)=\left\{\begin{array}{cc}
\frac{\sin (a+1) x+\sin 2 x}{2 x}, & \text { if } x0 \\
b & , \text { if } x=0 \\
\frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x0
\end{array}\right.
\]
If \( f \) is continuous at \( x=0 \), then the value of \( a+b \) is equal to
(a) \( -\frac{5}{2} \)
(b) -2
(c) -3
(d) \( -\frac{3}{2} \)
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