Question

Evaluate:

$\underset{x\to 0}{lim}(1+ax{)}^{\frac{1}{x}}$

• A. $e^a$
• B. $e^{\frac{1}{a}}$
• C. $1$
• D. None of these

Answer 1

The correct option is A $e^a$

Now,

$\underset{x\to 0}{lim}(1+ax{)}^{\frac{1}{x}}$

$={\left(\underset{ax\to 0}{lim}\right(1+ax{)}^{\frac{1}{ax}})}^a$

$=e^a$.