Question

Evaluate:

$\underset{x\to 0}{lim}{(1+\frac{x}{2})}^{\frac{1}{x}}$

Answer 1

Now,

$\underset{x\to 0}{lim}{(1+\frac{x}{2})}^{\frac{1}{x}}$

$={\left\{\underset{x\to 0}{lim}{(1+\frac{x}{2})}^{\frac{2}{x}}\right\}}^{\frac{1}{2}}$

$=e^{\frac{1}{2}}$.