Explanation

(c)
Given, $\lim_{x \rightarrow 0}\frac{\log{(3 + x) - \log{(3 - x)}}}{x} = k$
using L’ Hospital’s rule
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lim_{x \rightarrow 0}\frac{\left( \frac{1}{3 + x} + \frac{1}{3 - x} \right)}{1} = k$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{3} + \frac{1}{3} = k\ \ \ \ \Rightarrow \ \ \ \ \ \ k = \frac{2}{3}$