The value of p and q for which the function $f(x) = \begin{cases} \frac{\sin (p+1) x + \sin x}{x} &, x < 0 \\ \; \; \;\; \;q &, x = 0 \\ \frac{\sqrt{x+x^2} - \sqrt{x}}{x^{3/2}} & , x > 0 \end{cases}$ <br> is continuous for all $x$ in $R$, is

Question

( A ) $p = -\frac{1}{2}, q = \frac{3}{2}$
( B ) $p = -\frac{3}{2}, q = \frac{1}{2}$
( C ) $p = \frac{1}{2}, q = -\frac{3}{2}$
( D ) $p = -\frac{5}{2}, q = \frac{1}{2}$