The values of p and q for which the function

Question:

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

  1. $\mathrm{p}=-\frac{3}{2}, \mathrm{q}=\frac{1}{2}$

  2. $\mathrm{p}=\frac{1}{2}, \mathrm{q}=\frac{3}{2}$

  3. $\mathrm{p}=\frac{1}{2}, \mathrm{q}=-\frac{3}{2}$

  4. $\mathrm{p}=\frac{5}{2}, \mathrm{q}=\frac{1}{2}$

Correct Option: 1

Solution:

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