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JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to \infty }{\mathop{\lim }}\,\left[ \frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+.......+{{n}^{3}}}{{{n}^{4}}} \right]=\]

    A)                 \[\frac{1}{2}\]

    B)                 \[\frac{1}{3}\]

    C)                 \[\frac{1}{4}\]

    D)                 None of these

    Correct Answer: C

    Solution :

                    \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{\left( 1+\frac{1}{n} \right)}^{2}}}{4}=\frac{1}{4}.\]


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