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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{\ln {{(1+x)}^{1+x}}}{{{x}^{2}}}-\frac{1}{x} \right)=\]

    A) 0                     

    B) 1

    C) 2                     

    D) 1/2       

    Correct Answer: D

    Solution :

    [d]: Given limit \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{(1+x)ln(1+x)-x}{{{x}^{2}}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{ln(1+x)}{2x}\]                       (By L' Hospitals Rule) \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{2}\ln {{(1+x)}^{\frac{1}{x}}}=\frac{1}{2}\]


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