Question

The function `f(x) = (log(1+ax)-log(1-bx))/x` is not difined at x = 0. The value which should be assigned to f at x = 0, so that it is continuous at x = 0, is
A. `a - b`
B. ` a+ b`
C. `log a+lig b`
D. None of these

Answer 1

Correct Answer - B
For f(x) to be continuous, we must have
`f(0) = underset( x to 0) lim f(x) `
=` underset( x to 0) lim (log (1+ ax) - log (1-bx))/x `
` = underset( x to 0) lim (alog(1+ ax))/(ax)+(b log(1-bx))/(-bx)`
` = a*1 + b*1 ["using" underset( x to 0) lim (log (1+x))/x = 1]`
= a + b
` :." " f(0) = (a+ b) `