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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • 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 continuos at \[x=0\], is [IIT 1983; MP PET 1995; Karnataka CET 1999; Kurukshetra CEE 2002; AMU 2002]

    A)            \[a-b\]

    B)            \[a+b\]

    C)            \[\log a+\log b\]

    D)            \[\log a-\log b\]

    Correct Answer: B

    Solution :

               Since limit of a function is \[a+b as \]as \[x\to 0,\] therefore to be continuous at a function, its value must be \[a+b\] at \[x=0\]  \[\Rightarrow \,\,f(0)=a+b.\] 


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