A) \[\cos \,\,\sqrt{x}\]
B) \[1/(2\,\sin \sqrt{x})\]
C) \[(\cos \sqrt{x})/2\sqrt{x}\]
D) \[\sin \sqrt{x}\]
Correct Answer: A
Solution :
\[\underset{h\to 0}{\mathop{\lim }}\,\,\,\frac{\sin \sqrt{x+h}-\sin \sqrt{x}}{h}\] Applying Hospital?s rule, \[=\underset{h\to 0}{\mathop{\lim }}\,\,\,\frac{\frac{\cos \,\sqrt{x+h}}{2\sqrt{x+h}}}{1}=\frac{\cos \,\sqrt{x}}{2\sqrt{x}}\]You need to login to perform this action.
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