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

Explanation

We have given:
f(x)=`(log(1+a x)-"log"(1-b x))/x` , if `x!=0` and

k if x=0 is continuous at x=0

`=(log(1+a x)-log(1-b x))/x`

`=lim_(x->0)(log(1+a x)-log(1-b x))/x`

Apply L-Hospital Rule

`=lim_(x->0)(a/(1+a x)+b/(1-b x))/1`

`=a/1+b/1=a+b`