The values of $p$ and $q$ for which the function $f(x)=\left\{\begin{array}{1 1}\large\frac{\sin(p+1)x+\sin x}{x} & x < 0 \\ q & x=0 \\ \large\frac{\sqrt{x+x^2}-\sqrt x}{x^3/2} & x > 0 \end{array}\right.$ is continuous for all $x\;in\;R$ are

Question

$\begin{array}{1 1}(a)\;p=5/2,q=1/2&(b)\;p=-3/2,q=1/2\\(c)\;p=1/2,q=3/2&(d)\;p=1/2,q=-3/2\end{array}$