# How do you find lim (x+5)(1/(2x)+1/(x+2)) as x->0^+ using l'Hospital's Rule or otherwise?

${\lim}_{x \to {0}^{+}} \left[\left(x + 5\right) \left(\frac{1}{2 x} + \frac{1}{x + 2}\right)\right] =$
$= {\lim}_{x \to {0}^{+}} \left[\frac{x}{2 x} + \frac{x}{x + 2} + \frac{5}{2 x} + \frac{5}{x + 2}\right] = + \infty$
From the sum in the second line the first two expressions coverge to $\frac{1}{2}$ and $0$ respectively, the last two expressions diverge to $+ \infty$