Question

Solve:
$\underset{x\to 0}{lim}\frac{e^x-e^{-x}}{x}$

Answer 1

$\underset{x\to 0}{lt}\frac{e^x-e^{-x}}{x}$ [$\frac{0}{0}$- L hospital apply]

$\underset{x\to 0}{lt}\frac{\frac{d}{dx}(e^x-e^{-x})}{\frac{d}{dx}\left(x\right)}$

$\Rightarrow \frac{e^x-e^{-x}(-1)}{1}$

$\Rightarrow \frac{1-(-1)}{1}=2$.