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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    \[\underset{h\to 0}{\mathop{lim}}\,\frac{\sin \,\sqrt{x+h}-\sin \,\sqrt{x}}{h}\] is equal to

    A)  \[\cos \,\,\sqrt{x}\]

    B)  \[1/(2\,\sin \sqrt{x})\]

    C)  \[(\cos \sqrt{x})/2\sqrt{x}\]

    D)  \[\sin \sqrt{x}\]

    Correct Answer: A

    Solution :

    \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\frac{\sin \sqrt{x+h}-\sin \sqrt{x}}{h}\] Applying Hospital?s rule, \[=\underset{h\to 0}{\mathop{\lim }}\,\,\,\frac{\frac{\cos \,\sqrt{x+h}}{2\sqrt{x+h}}}{1}=\frac{\cos \,\sqrt{x}}{2\sqrt{x}}\]


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