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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x}{\sqrt{1+x}-\sqrt{1-x}} \right)\]is equal to

    A)  0                                            

    B)  1

    C)  2                            

    D)         \[-1\]

    E)  \[-2\]

    Correct Answer: B

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\times \frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x(\sqrt{1+x}+\sqrt{1-x})}{1+x-1+x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{x(\sqrt{1+x}+\sqrt{1-x})}{2x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\] \[=\frac{2}{2}=1\]


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