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JEE Main & Advanced JEE Main Paper (Held on 09-4-2019 Afternoon)

  • question_answer
    If \[f:R\to R\] is a differentiable function and \[f(2)=6,\]then\[\underset{x\to 2}{\mathop{\lim }}\,\int\limits_{6}^{f(x)}{\frac{2tdt}{(x-2)}}\]is:-                                                 [JEE Main 9-4-2019 Afternoon]

    A) 0                                 

    B) 2f'(2)

    C) 12f'(2) 

    D) 24f'(2)

    Correct Answer: C

    Solution :

    \[\underset{x\to 2}{\mathop{\lim }}\,\frac{\int\limits_{6}^{f(x)}{2tdt}}{x-2}\]           L Hopital Rule             \[\underset{x\to 2}{\mathop{\lim }}\,\frac{2f(x)f'(x)}{1}=2f(2)=f'(2)=12f'(2)\]      


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