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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    If \[f:R\to R\] be a differentiable function such that \[f(4)=6\] and  \[f'(4)=2,\] then \[\underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{x\,\,f(4)-4f(x)}{x-4}\]is equal to

    A)  \[2\]

    B)  \[-2\]

    C)  \[0\]

    D)  \[1\]

    Correct Answer: B

    Solution :

    \[\underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{x\,f(4)-4f(x)}{x-4}\] \[=\underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{f(4)-4f'(x)}{1}\] \[=f(4)-4f'(4)\] \[=\frac{6-4(2)}{1}=6-8\] \[=-2\]


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