Question

The value of $\underset{x\to 0}{lim}\frac{\log \left(5+x\right)-\log \left(5-x\right)}{x}$

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $0$
• D. Does not exist

Answer 1

Answer: (B)

$\frac{2}{5}$

When we substitute x=0 ; given limit is in the form $\frac{0}{0}$

$\Rightarrow$apply L-Hopitals rule

$\Rightarrow {lim}_{x\to 0}\frac{\frac{1}{5+x}.1-\frac{1}{5-x}.-1}{1}$

Now substitute x=0

$\Rightarrow \frac{1}{5}+\frac{1}{5}$

$=\frac{2}{5}$