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