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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    The function \[f(x)=\frac{\log (1+ax)-\log (1-bx)}{x}\] 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)  \[\log a+\log b\]                             

    D)  \[0\]

    Correct Answer: B

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\underset{x\to 0}{\mathop{\lim }}\,\frac{\log (1+ax)-\log (1-bx)}{x}\] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\frac{a}{1+ax}+\frac{b}{1-bx}}{1}\] \[=a+b\]


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