1. Tardigrade
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  4. The function f(x)=( log (1+a x)- log (1-b x)/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

Q. The function $f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}$ 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

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Solution:

The function $f ( x )$ is not defined at $x =0$ The function $f(x)$ is to be continuous, then,
$f (0) =\displaystyle\lim _{x \rightarrow 0} f(x)=\displaystyle\lim _{x \rightarrow 0}\left(\frac{\log (1+a x)-\log (1-b x)}{x}\right)$
$=\displaystyle\lim _{x \rightarrow 0}\left(\log \left(\frac{1+a x}{a x}\right) \cdot a-\frac{\log (1-b x)(-b)}{-b x}\right)$
$=\log _{e} e . a-\log _{e} e .(-b)= a + b$

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