For the function `f(x)=(log_(e)(1+x)+log_(e)(1-x))/(x)` to be continuous at x = 0, the value of f(0) is

Options

A. `-1`
B. 0
C. `-2`
D. 2

Answer

B

Explanation

Since the function f(x) is continuous at x = 0
`therefore f(0) =RHL =LHL`
Now, `RHL = lim_(h to 0) (log(1+0+h)+log(1-0-h))/(0+h)`
`=lim_(h to 0)(log(1+h)+log(1-h))/(h) `
`=lim_(h to 0) ((1)/(1+h)-(1)/(1-h))/(1)=0 " " ` [by L' Hospital's rule]
`therefore f(0) =RHL=0`