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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    The value of n such that \[\underset{x\to 3}{\mathop{\lim }}\,\,\frac{{{x}^{n}}-{{3}^{n}}}{x-3}=108\]is

    A)  \[3\]               

    B)  \[7\]

    C)  \[6\]              

    D)  \[4\]

    Correct Answer: D

    Solution :

    \[\underset{x\to 3}{\mathop{\lim }}\,\,\frac{{{x}^{n}}-{{3}^{n}}}{x-3}=108\] \[\Rightarrow \] \[\underset{x\to 3}{\mathop{\lim }}\,\,\,\frac{n{{x}^{n-1}}}{1}=108\] \[\Rightarrow \] \[n{{3}^{n-1}}=108={{4.3}^{(4-1)}}\] \[\Rightarrow \] \[n=4\]


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