MCQ
The value of $p$ and $q$ for which the function
$f(x)=\left\{\begin{array}{ll}\frac{\sin (p+1) x+\sin x}{x}, & x<0 \\q, & x=0 \\\frac{\sqrt{x+x^2}-\sqrt{x}}{x^{3 / 2}}, & x>0\end{array}\right.$
is continuous for all x in R, are
$f(x)=\left\{\begin{array}{ll}\frac{\sin (p+1) x+\sin x}{x}, & x<0 \\q, & x=0 \\\frac{\sqrt{x+x^2}-\sqrt{x}}{x^{3 / 2}}, & x>0\end{array}\right.$
is continuous for all x in R, are
- A$p=\frac{1}{2}, q=-\frac{3}{2}$
- B$p=\frac{5}{2}, q=\frac{1}{2}$
- ✓$p=-\frac{3}{2}, q=\frac{1}{2}$
- D$p=\frac{1}{2}, q=\frac{1}{2}$