If the function `f(x)` defined by `f(x)={(log(1+a x)-log(1-b x))/x ,\ \ \ if\ x!=0\ \ \ \ \ \ \ \ \ \ \ \ k ,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ x=0` is continuous at `x=0` , find `k` .

Explanation

`f(0)=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{a log (1+a x)}{a x}+frac{b log (1-b x)}{-b x}`


`=a cdot 1+b cdot 1` using, `.lim _{x rightarrow 0} frac{log (1+x)}{x}=1`


`=a । b`


`f(0)=(a+b)`