JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1+x)}^{n}}-1}{x}=\] [Kurukshetra CEE 2002]

    A)                 n

    B)                 1

    C)                 ?1

    D)                 None of these

    Correct Answer: A

    Solution :

                       \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(1+nx+{{\,}^{n}}{{C}_{2}}{{x}^{2}}+...\text{higher powers of }x\text{ to }{{x}^{n}})-1}{x}=n\].                 Aliter : Apply L-Hospital?s rule.


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