JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{x}^{n}}+1}\] where \[x<-1\] is [J & K 2005]

    A)                 ½

    B)                 ?1/2

    C)                 1

    D)                 None of these

    Correct Answer: C

    Solution :

                    \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{x}^{n}}\left( 1+\frac{1}{{{x}^{n}}} \right)}=\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{\left( 1+\frac{1}{{{x}^{n}}} \right)}=1\].


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