Q. $\lim_{h \rightarrow 0}\frac{\sin{\sqrt{x + h} - \sin\sqrt{x}}}{h}$ is equal to
A) $\cos\sqrt{x}$
B) $1/(2\sin\sqrt{x})$
C) $(\cos\sqrt{x})/2\sqrt{x}$
D) $\sin\sqrt{x}$
Explanation
(c)
$\lim_{h \rightarrow 0}\frac{\sin{\sqrt{x + h} - \sin\sqrt{x}}}{h}$
Applying L’Hospital’s rule,
$= \lim_{h \rightarrow 0}{\frac{\frac{\cos\sqrt{x + h}}{2\sqrt{x + h}}}{1} =}\frac{\cos\sqrt{x}}{2\sqrt{x}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.