Q80 / 180 · KCET 2009 · Mathematics

The function $f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}$ is not defined at $\mathrm{x}=0$. The value which should be assigned to $\mathrm{f}$ at $\mathrm{x}=0$ so that it is continuous at $\mathrm{x}=0$ is

  • A
    $a-b$
  • Correct answer
    B
    $a+b$
  • C
    $\log a+\log b$
  • D
    0

Solution

$\begin{aligned} \lim _{x \rightarrow 0} f(x) &=\lim _{x \rightarrow 0} \frac{\log (1+a x)-\log (1-b x)}{x} \\ &=\lim _{x \rightarrow 0} \frac{\frac{a}{1+a x}+\frac{b}{1-b x}}{1} \\ &=a+b \end{aligned}$

Hence, the correct answer is option: 'B'.

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