Question

lf $\underset{x\to 0}{lim}\frac{\log (3+x)-\log (3-x)}{x}=K$, then the value of $K$ is:

• A. $-\frac{2}{3}$
• B. $0$
• C. $-\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is D $\frac{2}{3}$

$\underset{x\to 0}{lim}\frac{log3(1+\frac{x}{3})-log3(1-\frac{x}{3})}{3\frac{x}{3}}$
$=\underset{x\to 0}{lim}\frac{1}{3}(\frac{log(1+\frac{x}{3})}{\frac{x}{3}}-\frac{log(1-\frac{x}{3})}{\frac{x}{3}})$
$useformula,\underset{x\to 0}{lim}\frac{log(1+x)}{x}=1$

$=\frac{2}{3}$