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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        The function\[f(x)=\frac{ln(1+ax)-ln(1-bx)}{x}\]is not defined at\[x=0\]. The value which should be assigned to\[f\]at\[x=0\]so that it is continuous at\[x=0,\]is

    A)  \[a-b\]                                

    B) \[a+b\]

    C)  \[ln\text{ }a+ln\text{ }b\]          

    D)  None of these

    Correct Answer: B

    Solution :

                    For\[f(x)\]to be continuous, we must have \[f(0)=\underset{x\to 0}{\mathop{\lim }}\,f(x)\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\log (1+ax)-\log (1-bx)}{x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{a\log (1+ax)}{ax}-\frac{b\log (1-bx)}{-bx}\] \[=a.1+b.1\]using, \[\left[ using\underset{x\to 0}{\mathop{\lim }}\,\frac{\log (1+x)}{x}=1 \right]\] \[=a+b\] \[\therefore \]  \[f(0)=(a+b)\]


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