Question

The function $f\left(x\right)=\frac{\log (1+ax)-\log (1-bx)}{x}$ is not defined at $x=0$. The value which should be assigned to $f$ at $x=0$ so that it is continuous there, is

• A. $a-b$
• B. $a+b$
• C. $\log a+\log b$
• D. none of these

Answer 1

Answer: (B)

$a+b$

$f\left(x\right)=\frac{\log (1+ax)-\log (1-bx)}{x}{lim}_{x\to 0}\frac{\log (1+ax)-\log (1-bx)}{x}={lim}_{x\to 0}\frac{\log (1+ax)}{ax\times \frac{1}{a}}+{lim}_{x\to 0}\frac{\log \left(1bx\right)}{-bx\times \frac{1}{b}}=a+b$