If the f(x)`=(log(1+ax)-log(1-bx))/x`,
`xne0` is continuous at x = 0 then, f(0) = .....

Options

A. loga - logb
B. a + b
C. loga + logb
D. a-b

Answer

B

Explanation

Given function
`f(x)=(log(1+ax)-log(1-bx))/x,xne0`
is continous at x=0
`thereforelim_(xto0)f(x)=f(0)` ….(i)
Here,
`lim_(xto0)f(x)=lim_(xto0)(log(1+ax)-log(1-bx))/x(0/0` form`)`
`=lim_(xto0)(a/(1+ax)-(-b)/(1-bx))/1` (Using L' Hospital's Rule)
`=lim_(xto0)(a/(1+bx)+b/(1-bx))=a+b`
From Eq. (i), we get
f(0)=a+b