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J & K CET Engineering J and K - CET Engineering Solved Paper-2005

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

    A)  \[1/2\]

    B)  \[-1/2\]

    C)  \[1\]             

    D)  None of these

    Correct Answer: C

    Solution :

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


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