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The value of \( p \) and \( q \) for which the function \( f(x)=\left\{\begin{array}{cl}\frac{\sin (p+1) x+\sin x}{x}, & x0 \\ q & , x=0 \text { is continuous for all } x \text { in } \\ \frac{\sqrt{x+x^{2}}-\sqrt{x}}{x^{3 / 2}} & , x0\end{array}\right. \)
P
\( \mathrm{R} \), are :
(1) \( p=\frac{1}{2}, q=-\frac{3}{2} \)
(2) \( p=\frac{5}{2}, q=\frac{1}{2} \)
(3) \( p=-\frac{3}{2}, q=\frac{1}{2} \)
(4) \( p=\frac{1}{2}, q=\frac{3}{2} \)
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