Question

$\underset{x\to 0}{\lim }\left(\frac{a^x-b^x}{x}\right)$ is equal to:

• A. 0
• B. 1
• C. $loga-logb$
• D. $loga/logb$
• E. does not exist

Answer 1

Answer: (C)

$\underset{x\to 0}{\lim }\frac{a^x-b^x}{x}=\underset{x\to 0}{\lim }\frac{a^x-x}{x}-\underset{x\to 0}{\lim }\frac{b^x-1}{x}$