A) \[\left( \frac{5}{2},\frac{1}{2} \right)\]
B) \[\left( -\frac{3}{2},-\frac{1}{2} \right)\]
C) \[\left( -\frac{1}{2},\frac{3}{2} \right)\]
D) \[\left( -\frac{3}{2},\frac{1}{2} \right)\]
Correct Answer: D
Solution :
\[RHL=\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{\frac{3}{2}}}}=\] \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\frac{\sqrt{1+x}-1}{{{x}^{{}}}}=\frac{1}{2}\] \[LHL=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (p+1)x+sinx}{x}=(p+1)+1=p+2\] for continuity \[LHL=RHL=f\left( 0 \right)\] \[\Rightarrow (p,q)=\left( \frac{-3}{2},\frac{1}{2} \right)\]You need to login to perform this action.
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