Question

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

• A. 2 log 5
• B. 1
• C. 0
• D. log 5

Answer 1

Answer: (D)

$\underset{x\to 0}{\lim }\frac{5^x-5^{-x}}{2x}$
Applying L- Hospital's rule
$=\underset{x\to 0}{\lim }\frac{5^x\log 5+5^{-x}\log 5}{2}$
$=\frac{\log 5+\log 5}{2}=\log 5$