Question

If $\displaystyle \lim_{ x\to0} \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)

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