How can I evaluate [math]\displaystyle\lim_{x \to \infty} \frac{e^ {1-\sin x} - e^{1 - \tan x}}{\tan x - \sin x}[/math]? How can one evaluate [math]\displaystyle\int_0^{\infty} \frac{\sin x}{x} \, e^{-x}\, dx[/math]?