If `f(x)={(log(1+a x)-log(1-b x))/x\ \ \ ,\ \ \ x!=0,\ \ \ \ \ \ \k\ \ \ \ \ \ \ \ \ \ \ \ \ \ ,\ \ \ \ \ \ \ \ \ \ \ x=0` and `f(x)` is continuous at `x=0` , then the value of `k` is `a-b` (b) `a+b` (c) `loga+logb` (d) none of these

Explanation

Given,

`lim_x→0​f(x)=lim_x→0​{(log(1+a x)-log(1-b x))/x}`

` =lim_x→0​[(log(1+ax))/x​−(log91−bx)/x​] `

`=lim_x→0​[a.(log(1+ax))/(ax)​+b.(log{1+(−bx))/((−bx)})]`


` =a×1+b×1 `

`=a+b`


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