Question

The value of $\underset{x\to 0}{lim}\frac{5^x-5^{-x}}{2x}$ is

• A. $\log 5$
• B. $0$
• C. $1$
• D. $2\log 5$

Answer 1

The correct option is A $\log 5$

$\underset{x\to 0}{lim}\frac{5^x-5^{-x}}{2x}$ .....$\left(\frac{0}{0}\text{form}\right)$
Applying L'Hospital's rule
$=\underset{x\to 0}{lim}\frac{5^x\log 5+5^{-x}\log 5}{2}$
$=\frac{\log 5+\log 5}{2}=\log 5$