Question

The function $f\left(x\right) = \frac{ln \left(1+ax\right)- ln\left(1 - bx\right) }{x} $ is not defined 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. ln a - ln b
• D. none of these

Answer 1

Answer: (B)

For $f (x)$ to be continuous at $x = 0$
$f(0) =\displaystyle \lim_{x \to 0} f(x) $
$= \displaystyle \lim_{x \to 0} \frac{ln\left(1+ax\right) - ln\left(1-bx\right)}{x}$
$ \left[\text{Using} \lim_{x \to0} \frac{\ln\left(1+x\right)}{x} = 1\right] $
$ = a+b $