Question

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

• A. log 5
• B. 0
• C. 1
• D. $2log5$

Answer 1

Answer: (A)

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