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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

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

    A)  2                                            

    B)  \[-2\]

    C)  \[-4\]                                   

    D)  3

    Correct Answer: C

    Solution :

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


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