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JCECE Engineering JCECE Engineering Solved Paper-2006

  • question_answer
    Let\[f(2)=4\] and \[f'(2)=4\]. Then\[\underset{x\to 2}{\mathop{\lim }}\,\frac{x\,\,f(2)-2f(x)}{x-2}\]is given by:

    A) \[2\]                                     

    B) \[-2\]

    C) \[-4\]                                    

    D) \[3\]

    Correct Answer: B

    Solution :

    \[\underset{x\to 2}{\mathop{\lim }}\,\frac{x\,\,f(2)-2f(x)}{x-2}\] \[=\underset{x\to 2}{\mathop{\lim }}\,\frac{x\,\,f(2)-2f(2)+2f(2)-2f(x)}{x-2}\] \[=\underset{x\to 2}{\mathop{\lim }}\,\frac{(x-2)f(2)}{x-2}-2\underset{x\to 2}{\mathop{\lim }}\,\frac{f(x)-f(2)}{x-2}\] \[=f(2)-2f(2)\] \[=4-2\times 4=-4\]


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