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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 43

  • question_answer
    If f is a continuous function in \[[0,1]\] such that \[f\left( \frac{1}{k} \right)=k\,\,\forall k\in N,\] then \[\underset{n\to \infty }{\mathop{\lim }}\,f\left( \sqrt[3]{{{n}^{2}}-{{n}^{3}}}+n \right)\] is equal to

    A) \[1\]                 

    B)        \[2\]

    C) \[3\]     

    D) \[4\]

    Correct Answer: C

    Solution :

    [c] As \[n\to \infty \,\,\,\underset{n\to \infty }{\mathop{\lim }}\,(\sqrt[3]{{{n}^{2}}-{{n}^{3}}}+n)=\frac{1}{3}\] \[\therefore \,\,\,\,\,\,\,\underset{n\to \infty }{\mathop{\lim }}\,f\left( \sqrt[3]{{{n}^{2}}-{{n}^{3}}}+n \right)=f\left( \frac{1}{3} \right)=3\]   


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