Question

If $\underset{x\to 0}{\lim }\frac{\log \left(3+x\right)-\log \left(3-x\right)}{x}=k,$ the value of k is

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

Answer 1

Answer: (D)

$\underset{x\to 0}{\lim }\frac{\log \left(3+x\right)-\log \left(3-x\right)}{x}=K$ (by L 'Hospital rule)
$\Rightarrow \underset{x\to 0}{\lim }\frac{\frac{1}{3+x}-\frac{-1}{3-x}}{1}=K\therefore \frac{2}{3}=K$